COMBINATIONS - DISCRETE MATHEMATICS
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- เผยแพร่เมื่อ 6 ก.ย. 2024
- In this video we introduce the notion of combinations and the "n choose k" operator.
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Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.
![[Discrete Mathematics] Permutations and Combinations Examples](http://i.ytimg.com/vi/FCYj10HuA_E/mqdefault.jpg)
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i've literally spent the last 2 weeks crying because i couldn't understand this chapter and after watching this video i finally understand it thank you!
I'm loving this series, and am finding it so helpful - thank you! One minor point is that in the lottery example (from memory) your odds is actually the probability (p). The odds = p / 1 - p
SFU REPRESENT!! ( you were my TA for linguistics)
Still haven't forgotten who you are. Try me again in about 5 years lol.
TheTrevTutor duly noted. I have Binay right now and struggling a lot for MACM.
Time to try him again
@@nopecharon haha one more year to go
THE TIME HAS COME@@splashdot1894
Can't reply to your comment since you don't have it enabled.
You will not have consecutive vowels in the final product. We arrange the vowels, then we chose 5 out of the 7 available positions to put those vowels. xTxLxLxHxSxSx. The vowels will replace 5 out of those 7 x's. We had to arrange the vowels independently so we know how to order them.
This series has helped understand the entire scenario of these permutations and combinations i couldn't understand for years.
The last example was amazing! You just know where a person might get confused and you make it clear immediately. Thank you so much
This video is 8 years old, and even today u r the best even to this day.
Personally, I do like your voice.
Thanks, dude. I really appreciate your concise explanations to all of these different concepts...got a test in 5 hours...hope I don't fail lol
4 years late but... How was the test??? XD
@@capriphonix8863 😂😂😂
@@capriphonix8863 🤣
@@capriphonix8863 😂😂😂
TELL US HOW THE TEST WENT!
I was ready to cry because I have an exam in a few days and I couldn't make any sense of the textbook or the examples. Thank you so much for these videos, you're a lifesaver!
yup now I understand.I have to use principle of product rather than principle of addition to solve it....thanks a lot sir
This channel deserves more subs!
Im just taking the course just its my last class for my IT degree
I really dont like math but ur vids are helping me though it
These are awesome, my teacher gave a similar example as the last example , couldn't understand and doing it on my own before watching this video ❤❤❤
This was super helpful and very insightful.
You're a life saver Trev!
Your channel deserves millions of subs
just keep going with your videos ,they are really helpful
You saved me !
I am going to be your biggest advocate...
Why did I not find you before? PS:Midterms are tomorrow and tonight I will be pullling an all nighter.
17:20 I'm Weird. :(
Is the last exercise a mixture of combinations and permutations? When we compute how many arrangements we can do with the vowels and the consonants?
I love your voice man
I'm watching because I'm writing a Discrete Math exam tomorrow and haven't started yet.
Thank you so much for your teaching, I understand more on this topic, yeay! Hope I can excel my exam tomorrow. Btw, I love your video because you explain clearly and also because of your voice, sorry being weird. hahahhahaa
@10:40
what's the probability of drawing 5 cards such that 3 be diamonds and 2 clubs?
Don't returner the card you draw.
+TrevTutor,
Hey Trev Tutor, I am confused with this problem “what are the odds of winning a lottery where all 6 numbers of chosen out of 49 must be picked to win”? Wouldn’t this be a permutation question since lottery number such 123456 will be different from a lottery number of 654321. So order matters? Thank you for your awesome video!
Does order matter in most lotteries around the world? I've never seen a lottery where order matters. Normally you pick 6 numbers and then they just have to match to win. When I remake this, I'll be more specific.
i was wondering the same
at minute 15:24 i don't get why he multiplies by 7choose5? order does matter in my opinion because AAAEE in the first five positions is a different arrangement than AAAEE from the 2nd position until the 6th. Probably I'm wrong here, I just don't get why...
I love the liberty mutual commercials in the middle of the videos 😂😂😂♥️
I'll be watching this video under so much stress for my finals and this guy here is like "maybe you are watching this because you find math cool or my voice " yeahh it has to be your voice 😅
in the last example you made a combination for the vowels letters, but in this case we will have consecutive vowels!! can you explain that further please ? :)
going to be honest i have a final exam on this in an hour and I absolulty hate this course. Im going to fail it for the second time and just need to pass it so I can take my require CSC courses to finally graduate. Your videos do help but Its hard for me to think in this type of way
When I first saw the last problem prompt, I immediately thought something like Total Arrangements - Arrangements where vowels are all consecutive. But I can't get this to work. The number is way off.
Total Arrangements = 11! / ( 1! * 3! * 2! * 1! * 2! * 2! )
Arrangements with Vowels Grouped = 5!/ (3! * 2!) * 6!
831,600 - 7200
vs
the video formula was 37800.
after writing this out, does this not work because there are some subsets in total arrangements where vowels are partially consecutive? I need to somehow exclude those as well?
Thank you so much! Your video lessons is helping me prepare for a tech interview at Google.
same :)
same
why does the last problem involve combination. I thought combination is only necessary when you need to not have two similar permutations. for example BAS would be the same as BSA
+MrBrN197 Objects can't be beside each other. So we use combinations to to choose the positions of the letters.
+TheTrevTutor what i don't understand is when we have seven spaces for the vowels, they are already separated. so if i have 5 letters at first I have 7 places to put the letter then i have 6 places to put the second letter and it still will not be near the first letter. If i have seven spaces for vowels and for my first letter I put A right at the start, I can put the next letter anywhere in the next 6 spaces without it coming into contact with "A" because T is in the way. and lets say the next vowel is E and i put it right after T i still have 5 spaces to put another vowel anywhere in those 5 spaces without it touching either "A" or "E". so i would have thought it is a simple as 7x6x5x4x3 ... divided by 2!x3! (for the permuations of "AAA"and "EE"). I've understood other example on your permutation and combinations except this one.
+MrBrN197 I'm approaching it in this manner. I want to sort all of the consonants. Then I want to sort all the vowels. Now I want to choose spots for my vowels. If your method comes up with the same numeric result in the end, then it's probably fine. However, the method I'm giving is a more intuitive approach that isn't going to get much more complicated if I increase the difficulty of the problem.
+TheTrevTutor that's just what I was thinking. That both out methods would get the same result.. I also use a 4 letter word and did the example using my method and also manually and got the correct result. In my mind my method seems to make more sense. Thanks for quick feedback aswell
+MrBrN197 & +TheTrevTutor Maybe I'm missing something here but
7!/3!2! = 420
AND
(6! / (2! 2!)) * (7! / ((7 - 5)!) * (5! / (3! 2!)) = 4,536,000.
Therefore, the solutions are not equivalent.
Or should I have used nCr instead of nPr? Giving me instead
(6! / (2! 2!)) * (7! / ((7 - 5)! * 5!) * (5! / (3! 2!)) = 37,800
but still they don’t equal each other.
+MrBrN197 please show the full Permutation, I feel like I’m not understanding something. Thanks
what if we place first the vowels and then we put between them the consonats ?? i think is a differents answer because ou sont have to choose but why>?
because we want no two consecutive vowels, not no consecutive constants. so you cannot apply the same logic in this case.
why did we use combination in the arrangement problem if order does matter here
5:20 I forgot that method of multiplication existed!!!
your content is really helpful. appreciate it✊
hello thank you so much for this video; i have one question . for the last exercise why did you say the order does not matter ? don't we have the word "arrangement" which means that the order matters ?? thank you
the question at 10:00, how many ways to draw 3 diamonds and 2 clubs?
How does this question not involve 52 at all? I never would have guessed to do 13 choose from bla bla bla. I would have done 52 choose bla bla bla
+atribecalled solitude i hope i can explain what i understood , you want to draw 3 diamonds from only 13 not 52 ,and also you want to draw 2 clubs from only 13 not 52 because it has only 13 diamonds and 13 clubs only and this all the possibility of drawing , i hope this explanation is clear
You're thinking about probability the probability of getting that hand would be the number of successful combinations over 52 choose 5. We just wanted to know all the different ways I could end up with that hand. So there are multiple ways to draw it but there are a lot more ways to draw 5 from a deck. You were probably wondering why the number is so big when the chance of doing so is small that's why.
I think it means how many possible hands have 3 diamonds and 2 clubs?
At 7:30 you said its a combination but given that cards have suites wouldn't that mean its a permutation because a 5 of hearts is not the same as a 5 of spades
Preyliens We're just picking five different cards out of a deck to form a hand. When you make a hand in any card game, order doesn't matter, so it's a combination.
in the last example, what is the purpose of (5!)/(3!2!)?. we already got the arrangement in (6!/2!2!)7C5, don't we?
6!/(2!2!) is for arranging the 6 consonants. 7C5 is for choosing 5 vowels out of 7. However, since the vowels are not identical, we can arrange the vowels too. Hence, the arrangement of the vowels is 5!/(3!2!).
last question is very good. Thanx a lot sir.
THE Question: what are the odd of winning a lottery where all numbers chosen out of 49 must be picked to win ?
i dont understand how odds affect the answer can u explain?
I'm not sure I understand what you mean. "odds" means "chance", so it's a probability question rather than just counting.
hi, I have a question 17:33 about "TALLAHASSEE" with no consecutive vowels
I think it is [6!/(2!*2!)]*C(7,3)*C(10,2) since "no consecutive vowels"
can you help me out with this?
I think C(7,5) because there are 7 places to put 5 vowels. How many combinations y get by choosing 5 numbers out of 7 numbers.
you are a god amongst men.
Hello, I don't know where to post my questions, I'm being challenged by this question, I was wondering if you could help me with it.
"Eight married couples are standing in a room. If four people are chosen at random, what is the probability that:
I) Exactly one married couple is among the four?
ii) no married couple is among the four?
you do have a nice voice
I have a doubt regarding the last question. What if we find all the arrangements of the word "TALLAHASSEE" and subtract the arrangements where consecutive vowels occur?.
Thanks in Advance.!!
So by using permutation we can find all the number of the arrangements of the word, but I think it's too hard If there is a way to find the number of the arrangements where consecutive vowels occur
why can't I use (11! / 2! . 2! . 5!) fact 5 for the vowels treating them as if I can't tell the difference between As and Bs
What platform did you use to make this video?
ps; I need to make a short video explaining a basic concept in math for a project in school, but I dont know how or what app to use.
I would appreciate the help
On that last question, did you only use Combination with the (7 5) -purple-?
+Eduardo Wagner The combination is for picking which spots we want the vowels. The rest is ordered.
The last Tallahassee problem. The answer is the whole (6!/2!2!)(7/5)(5!/3!2!) there is no way to simplify? Is that an equation? could you not simplify the 6!/2!2!? or the other 5!/3!2! or multiply them?
Can you please explain in detail the 3 diamonds and 2 clubs question? I cant get the intuition for it.
There are 13 elements per suit. Diamond is one of the suits. We are choosing 3 out of those 13 diamonds. Therefore, (13 choose 3). Same thing with 2 clubs. There are a total of 13 clubs in a 52-card deck and we are choosing 2 out of those 13. Therefore, (13 choose 2). We are multiplying because it asks for 3 diamonds AND 2 clubs. If it would have been 3 diamonds OR 2 clubs, we would have added them together instead. I hope that helps.
@Lucas Watch the video on sum and product rules. If you're doing something subsequently, like picking x diamonds AND THEN y clubs it is usually multiplication. If the two things you're doing are seperate, like picking x diamonds OR y clubs or maybe making 2 playing hands where one has diamonds and the other has clubs then it will be addition.
Beautiful video!
for the choosing drawing 3 diamonds and 2 clubs, why can't you just do 13*12*11*13*12 ?
This is where i'm getting tripped up in my exams
how come you cancelled those numbers and adding another no?
we love your voice, you should make a rap math video about combinations and permutations!
i cannot understand when to stop how can i get to know when to stop
Amazing!
well ... actually ... yeah ... I love your voice and I know I'm weird
i didn't understand the meaning of "odds of winning " and i didn't understand the whole example can any one explain its meaning ?
+gehad mohsen "odds of winning" is the chance that all six of your numbers will be picked.
In the word "TALLAHASSEE" how to solve if we want to arrange the word in a circle with the same conditions given in the video ?
Same as solving TALLAHASSEE arrangements, but then divide by 11 for each possible rotation around a table.
why do we divide 6!/2!2!, i get that the numbers come from the Ls and Ss but why do we divide? 14:30
There are arrangements where simply the positions of the Ss or Ls are switched with eachother and then the word will still be the same since it's duplicate letters. We don't want those scenarios, we only want unique words, so therefore we do this division and will get a lower number of total arrangements because of it.
@@Fr0ggeh86 Thank you
Nice
"You're kind of weird, just kidding"
No no no... don't just kidding ... I am weird lol
i am honestly in love with you :')
ilu2
at 15:15 , by 7/5 u mean 7!/2!*5! right?
Yes
in 11:47 don't we care about the order, for example, 1,2,3,4,5,6 is a winning number but 2,1,3,4,5,6 isn't a winning number
so it should be 1/P(49,6) not 1/C(49,6)
I think it's because lottery numbers in that situation are considered a sets their only arranged in chronological order, so you can't have 2,3,4,5,6 and 1,2,3,4,5,6, as different numbers
How did you get 13 clubs and 13 diamonds?
In a pack of cards (52 cards), there are 13 clubs cards and 13 hearts, 13 spades, and 13 diamonds.
On the last Q, Why there is 7C5?
It is not 7P5? Could someone answer me please?
It is not 7P5? Could someone answer me please?
This Is Who I Am With Permutation order matters. The cards for example: A 1 2 3 4 5 are the same as 5 1 3 2 4 A. Just in a different order. Since order wasn't stated we use combinations.
I don't understand permutation is important for lotto tickets. The order does matter.
Lotteries here just draw "X" numbers and if they match then you win.
It’s not an option to take this course or not sadly
the ending 😭😭🤣
sir why not 13c3+13c2 instead of 13c3*13c2?
+Suvendu Deb These are consecutive events. We choose 3 from 13, then we choose 2 from 13. If they were occurring separately and didn't depend on each other, then we might add.
Lottomax eh? You must be from BC :P
the last problem was hard actually :/
+yasser osama Almost everything is hard the first few times you see it. However, when you are introduced with a problem like "this is hard", then some people tend to stop understanding it because they believe it's above them.
just wanted to say i had the TELEHASSEE question but with 10 women and 6 men where the men can't stand together :) i got it right thanks very much
10! * C(11,6) * 6! ??
By watching the last problem i saw how dumb i can be while trying to even understand the question.
I love you TrevTutor, you save my ass
13:43 "ofc we have a lot of ease otherwise i wouldn't have picked this question" major kek
I'm here for a purpose but I guess I'm kinda weird too xD
im cry laughing atm 🥴🥴🥴
lmao
Why is my $200 textbook worse at explaining stuff than this guy????
lol
You're kinda weird, lol