For the students with prizes problem, I saw it a bit differently. You choose 2 students out of 4 who will get prizes, so 4 choose 2. Then it's equivalent to putting 10 items into 2 boxes, with at least one item per box: x1 + x2 = 10, xi >= 1.
I thought the same, but it seems like he is considering every prize to be different. Your reasoning would work if u considered the prizes like identical points, he is considering every prize like it's a different letter/number.
In the arrangement question in the video, can u plz explain the difference between s2 and atleast 2 consecutive pairs? For me they appear same. s2 also means atleast 2 pairs are consecutive but we have a different formula given here in the video? please help
@@yasmin9718 no, what they mean is there is a 1/2^10 chance that all of the prizes go to one student and the other gets zero, in which case the premise that two students get prizes would be false. I too think that this scenario should have been excluded.
Yes, this case is included in S2 but it is also included in S3 which we subtract so we are left only with the cases where both students get at least one prize.
I know it's very late but leaving the answer for any future viewer: Exactly 2 (E2) means that in an arrangment of letters there should be only two pairs of consecutive letters. For eg : "ARRANGEEMNT" , but it does not allow the words like "AANRRGEEMNT" (here 3 pairs of consecutive letters are being counted and those are " A , R , E") and S2 only cares for the condition of 2 pairs of consecutive letters being allowed and does not stop from 3 pair of consecutive letters from being counted.
How is S3 ways in which 3 students are not getting prizes?? In all other examples s3=no of ways of actually happening of an event. Hope u make it clear
Hi, I know its too late but this is what's happening in the problem. Think of it like this, s2 gives the number of ways of more than 1 student getting the prize. s2 is not the number of ways of exactly 2 students getting the prize. That's the difference between E2 and S2. Hope this clarifies one of ur doubts. And also, we can think of s2 as the number of ways of atleast 2 students not getting the prize, s3 as the number of ways of atleast 3 students not getting the prize, this means that in case of s3, only 1 student got the prize, that is why its 1^10.... now subtracting s3 from s2 will give u the number of ways of exactly 2 students getting the prize, since subtracting the case "atleast 3 students not getting the prize "from "atleast 2 students not getting the prize" will give u the exactly 2 students getting the prize. which is the required answer. Hope it helps.
Also, this problem can be solved in an easier way... since we want exactly 2 students getting the prize, number of ways we can choose 2 students from 4 is 4C2. now each prize has 2 choices since there are 2 students. so its 2^10.. but we need to subtract 2 from 2^10 since there are two cases where one of the students may get all the 10 prizes. So the final answer will be (4C2) * ((2^10) - 2).
thanks for the reply but i am still confused. In the arrangement question in the video, can u plz explain the difference between s2 and atleast 2 consecutive pairs? For me they appear same. s2 also means atleast 2 pairs are consecutive but we have a different formula given here in the video? please help
I think this assumes that all 10 prizes are distinguishable, so you actually have 10 times a binary choice. If they weren’t distinguishable, it would be nCr (4,2) * nCr (11,2) (and then minus the overcounted) like in the cases where 10 were to be composed out of two integers. Right?
can u help me with this question? In how many ways can the 26 letters of alphabet be permuted so that none of the patterns CAR, DOG, PUN or BYTE occurs. Also, find the number of permutation of the 26 English alphabets which contain (i) Exactly three (ii) atleast three of the patterns CAR, DOG, PUN and BYTE.
![[Discrete Mathematics] Derangements](http://i.ytimg.com/vi/BOFWLhH0Igo/mqdefault.jpg)
![[Discrete Mathematics] Derangements](/img/tr.png)
![[Discrete Mathematics] Inclusion Exclusion Problems](/img/n.gif)
For the students with prizes problem, I saw it a bit differently.
You choose 2 students out of 4 who will get prizes, so 4 choose 2.
Then it's equivalent to putting 10 items into 2 boxes, with at least one item per box: x1 + x2 = 10, xi >= 1.
I thought the same, but it seems like he is considering every prize to be different. Your reasoning would work if u considered the prizes like identical points, he is considering every prize like it's a different letter/number.
does it matter for the final answer?@@lange1200
does it matter for the final answer?@@lange1200
In the arrangement question in the video, can u plz explain the difference between s2 and atleast 2 consecutive pairs? For me they appear same. s2 also means atleast 2 pairs are consecutive but we have a different formula given here in the video? please help
10:01 doesn't 2^10 include a cases in which either of the students would have zero prizes, while the other would have 10..?
each prize has the option either to go to student1 or student2, there is no third option to not go to neither of them
@@yasmin9718 no, what they mean is there is a 1/2^10 chance that all of the prizes go to one student and the other gets zero, in which case the premise that two students get prizes would be false. I too think that this scenario should have been excluded.
Yes, this case is included in S2 but it is also included in S3 which we subtract so we are left only with the cases where both students get at least one prize.
what is S2 exactly and how its 1^10?? not able to understand. :(
I wish I would have known about this earlier this term! It was so much help
why in S3 1^10 why 3^10 is wrong because it mean i distribute 10 prizes over three i rally don't understand this point ?
because S3 means 3 students do not have prizes, which only one students has all prices. (It is not mean 3 students has prizes..)
how?? S2 means two conditions getting satisfied?? can u elaborate?
I am also confused about students and prizes example. why is it ^10? Can you help me please TrevTutor?
what is the difference between Sm and Lm?
what is the difference between E2 and s2? S2 also means two pairs r together. getting confused
I know it's very late but leaving the answer for any future viewer:
Exactly 2 (E2) means that in an arrangment of letters there should be only two pairs of consecutive letters. For eg : "ARRANGEEMNT" , but it does not allow the words like "AANRRGEEMNT" (here 3 pairs of consecutive letters are being counted and those are " A , R , E") and S2 only cares for the condition of 2 pairs of consecutive letters being allowed and does not stop from 3 pair of consecutive letters from being counted.
How is S3 ways in which 3 students are not getting prizes?? In all other examples s3=no of ways of actually happening of an event. Hope u make it clear
Hi, I know its too late but this is what's happening in the problem. Think of it like this, s2 gives the number of ways of more than 1 student getting the prize. s2 is not the number of ways of exactly 2 students getting the prize. That's the difference between E2 and S2. Hope this clarifies one of ur doubts. And also, we can think of s2 as the number of ways of atleast 2 students not getting the prize, s3 as the number of ways of atleast 3 students not getting the prize, this means that in case of s3, only 1 student got the prize, that is why its 1^10.... now subtracting s3 from s2 will give u the number of ways of exactly 2 students getting the prize, since subtracting the case "atleast 3 students not getting the prize "from "atleast 2 students not getting the prize" will give u the exactly 2 students getting the prize. which is the required answer. Hope it helps.
Also, this problem can be solved in an easier way... since we want exactly 2 students getting the prize, number of ways we can choose 2 students from 4 is 4C2. now each prize has 2 choices since there are 2 students. so its 2^10.. but we need to subtract 2 from 2^10 since there are two cases where one of the students may get all the 10 prizes. So the final answer will be (4C2) * ((2^10) - 2).
thanks for the reply but i am still confused.
In the arrangement question in the video, can u plz explain the difference between s2 and atleast 2 consecutive pairs? For me they appear same. s2 also means atleast 2 pairs are consecutive but we have a different formula given here in the video? please help
please explain the first problem of the video too.
I think this assumes that all 10 prizes are distinguishable, so you actually have 10 times a binary choice. If they weren’t distinguishable, it would be nCr (4,2) * nCr (11,2) (and then minus the overcounted) like in the cases where 10 were to be composed out of two integers. Right?
s2 should be equal to 4c2*{2^10-1} in student prize problem .bcz there will one case when we are giving all prizes to 1 student.
can someone please elaborate on the counting mechanism of the students and prizes example ? @TheTrevTutor
can u help me with this question?
In how many ways can the 26 letters of alphabet be permuted so that none of the patterns CAR, DOG, PUN or BYTE occurs. Also, find the number of permutation of the 26 English alphabets which contain
(i) Exactly three (ii) atleast three of the patterns CAR, DOG, PUN and BYTE.
Do u still need the answer to this? It's too late but still, just asking haha
man I didn't understand the tasks but thanks for the formulas
you're awesome, thank you for sharing your genius
Thankyou so much, was very helpful:)
I believe you are using the formula in a wrong manner