He's selecting 6 cards at a time, so that's why the numerators are 6!. The first one shows the number of ways there could be 4 blue and 2 red, so we get 6!/(2!4!). The second one shows how many ways there could be 3 red & 3 blue, hence why it's 6!/(3!3!). Hope that helps.
Hey. The reason for the x5 in 2c is that there are just 5 different positions for the letter "U". Think of this as P(7,4) ways to arrange the other 4 letters, then x5 since there are 5 places the "U" can be placed. Hope that makes sense.
@@AlRichards314 Oh! Now I understand! Thank you! This will be a good reference. I was thinking about 5 unique numbers from 1-15. How many will be if all 5 numbers are in sequence.
When you use P(7,4) that's an arrangement of 7 object taken 4 at a time, So any 3 of those objects will not be in the arrangement. Question 3b says the T and H must be in the arrangement, so it's a lot like 2b. Notice that 2d's answer is just 2b's answer times 4x2.
Let's say it's Joe & Lisa (J & L) plus 6 other people. The easting will look something like this: J _ L _ _ _ _ _. There are 6 ways that cn occur down to _ _ _ _ _ _ J _ L. This 6 is the same as the number of other people. So there will b 6! x 6 x 2 ways for this to happen. The 6! is the number of other people and the 6 is the number of ways they can be one east apart. The x2 is because it can be J _ L or L _ J... Hope that make sense.
The P(6,6) which is 6! accounts for the number of ways to arrange 6 things, which is 1 couple and 5 other individuals. The x2 is because any 2 people can sit in 2 different ways. On the left of the pair or the right.
What I was trying to explain was that the 7 people is really one couple that are always together plus 5 other people, so there are 6 'things" to arrange, hence the P(6,6).
Hey. Don't be so hard on yourself. In example 2 b) SOUTHERN has 8 letters. If you take the S & N out there's only 6 letters left that you can put in the middle 3 spots. So the P(6,3) is 3 letters from O,U,T,H,E, and R, which is 6 letters.
Never knew that a 15min discussion would be better than listening to my prof for an hour..ty
I’m using this to prepare myself for the Mathletes Competition on November 16. It’s only 32 days away. Thanks for the vid! May God bless you.
TTV Ur Mom goodluck
How did you do?
how did u do
Thanks so much. This was so helpful and your explanations were easy really easy to understand
Thanks so much!! This helped me a lot plus your explanation is great!
Wow. This is very great explanation!
isnt the first one su[posed to be 4 factorial?
He's selecting 6 cards at a time, so that's why the numerators are 6!. The first one shows the number of ways there could be 4 blue and 2 red, so we get 6!/(2!4!). The second one shows how many ways there could be 3 red & 3 blue, hence why it's 6!/(3!3!). Hope that helps.
Hello! In 2C, why 5xP(7,4)? I thought i should be P(7,4)^5, (read as raise to 5). Thank you!
Hey. The reason for the x5 in 2c is that there are just 5 different positions for the letter "U". Think of this as P(7,4) ways to arrange the other 4 letters, then x5 since there are 5 places the "U" can be placed. Hope that makes sense.
@@AlRichards314 Oh! Now I understand! Thank you! This will be a good reference. I was thinking about 5 unique numbers from 1-15. How many will be if all 5 numbers are in sequence.
Clear and understandable! Thanks.
If you do P(6,6) for 3b then why don't you do 2 x P(7,4) for 2d by treating TH as a single object?
Is it because if you do 2 x P(7,4) it doesn't guarantee that TH or HT is in the word?
When you use P(7,4) that's an arrangement of 7 object taken 4 at a time, So any 3 of those objects will not be in the arrangement. Question 3b says the T and H must be in the arrangement, so it's a lot like 2b. Notice that 2d's answer is just 2b's answer times 4x2.
What if it says how will she be seated if they have to be seated one seat apart
Let's say it's Joe & Lisa (J & L) plus 6 other people. The easting will look something like this: J _ L _ _ _ _ _. There are 6 ways that cn occur down to _ _ _ _ _ _ J _ L. This 6 is the same as the number of other people.
So there will b 6! x 6 x 2 ways for this to happen. The 6! is the number of other people and the 6 is the number of ways they can be one east apart. The x2 is because it can be J _ L or L _ J...
Hope that make sense.
I understood this concept very nicely sir.
I understand it better than my math teacher...
In 3_b why we didnot multply by 6 for places
The P(6,6) which is 6! accounts for the number of ways to arrange 6 things, which is 1 couple and 5 other individuals. The x2 is because any 2 people can sit in 2 different ways. On the left of the pair or the right.
Okay but why in the previous example he multiply by 4 for places of th
I mean what is the differnce btw 2_d and this part
P(6,6) explaination could use some work
What I was trying to explain was that the 7 people is really one couple that are always together plus 5 other people, so there are 6 'things" to arrange, hence the P(6,6).
AlRichards314 but don’t TH also work as a couple? You didn’t have that as P(7,4).
On number one would it make a difference if the balls weren't identical
I mean the cards
Understandable🤗
I’m stupid I don’t know how you would get 6 in b
Hey. Don't be so hard on yourself. In example 2 b) SOUTHERN has 8 letters. If you take the S & N out there's only 6 letters left that you can put in the middle 3 spots. So the P(6,3) is 3 letters from O,U,T,H,E, and R, which is 6 letters.
@@AlRichards314 thanks I think I got the gist of it now thanks again
thank you sir
im about to take an difficult exam tomorrow
lol same, mines tomorrow as well
thank youuuuuuuuuuuuuuuuu...omg this chapter so cnfusing
other way for the first question: 7A6 / ( 4! * 3! )
Youssef Mankari, 5040/144 = 35. You are right, however I think he is trying to explain for lower leveled kids.