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Sammy has flavors of candies with which to make goody bags [#permalink]
16 Aug 2012, 22:53

Expert's post

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Difficulty:

85% (hard)

Question Stats:

43% (02:21) correct
57% (01:36) wrong based on 319 sessions

Sammy has x flavors of candies with which to make goody bags for Franks birthday party. Sammy tosses out y flavors, because he doesnt like them. How many different 10-flavor bags can Sammy make from the remaining flavors? (It doesnt matter how many candies are in a bag, only how many flavors).

(1) If Sammy had thrown away 2 additional flavors of candy, he could have made exactly 3,003 different 10-flavor bags. (2) x = y + 17

Re: Sammy has flavors of candies with which to make goody bags [#permalink]
16 Aug 2012, 23:32

3

This post received KUDOS

Expert's post

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Sammy has x flavors of candies with which to make goody bags for Franks birthday party. Sammy tosses out y flavors, because he doesnt like them. How many different 10-flavor bags can Sammy make from the remaining flavors? (It doesnt matter how many candies are in a bag, only how many flavors).

In order to calculate how many 10-flavor bags can Sammy make from the remaining (x-y) flavors, we should know the value of x-y. The answer would simply be \(C^{10}_{x-y}\). For example if he has 11 flavors (if x-y=11), then he can make \(C^{10}_{11}=11\) different 10-flavor bags.

(1) If Sammy had thrown away 2 additional flavors of candy, he could have made exactly 3,003 different 10-flavor bags. We are told that \(C^{10}_n=3,003\), where \(n=(x-y)-2\): he can make 3,003 10-flavor bags out of n flavors. Now, n can take only one particular value, so we can find n (it really doesn't matter what is the value n, important is that we can find it), hence we can find the value of x-y (x-y=n+2). Sufficient.

(2) x = y + 17 --> x-y=17. Directly gives us the value of x-y. Sufficient.

Re: Sammy has flavors of candies with which to make goody bags [#permalink]
17 Aug 2012, 01:17

Expert's post

Hey thanx. But I shall like to bother you again. I have come across around 3 questions of this type where the value of the total, of which we are supposed to make selection, is not known. Even in this question also, I knew that there could be only one value for which the answer comes out to be 3003, but since I was unable to come out with the solution, I sought help. So my question is that can't there be any more value for n for which nC10 is 3003? _________________

Re: Sammy has flavors of candies with which to make goody bags [#permalink]
17 Aug 2012, 01:30

Expert's post

siddharthasingh wrote:

Hey thanx. But I shall like to bother you again. I have come across around 3 questions of this type where the value of the total, of which we are supposed to make selection, is not known. Even in this question also, I knew that there could be only one value for which the answer comes out to be 3003, but since I was unable to come out with the solution, I sought help. So my question is that can't there be any more value for n for which nC10 is 3003?

Re: Sammy has flavors of candies with which to make goody bags [#permalink]
29 Dec 2013, 15:35

Marcab wrote:

Sammy has x flavors of candies with which to make goody bags for Franks birthday party. Sammy tosses out y flavors, because he doesnt like them. How many different 10-flavor bags can Sammy make from the remaining flavors? (It doesnt matter how many candies are in a bag, only how many flavors).

(1) If Sammy had thrown away 2 additional flavors of candy, he could have made exactly 3,003 different 10-flavor bags. (2) x = y + 17

Question stem basically says we have x-y flavors and we need to pick 10 out of these

How many combinations can we make?

Statement 1

So this is giving us the number of combinations of x-y-2, therefore we can imply what x-y is. Do we need the calculation? No, there will only be one number that will give this answer when deciding to pick 10 out of it.

Re: Sammy has flavors of candies with which to make goody bags [#permalink]
25 May 2015, 06:57

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