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Sammy has flavors of candies with which to make goody bags

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Sammy has flavors of candies with which to make goody bags [#permalink] New post 16 Aug 2012, 22:53
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43% (02:21) correct 57% (01:38) wrong based on 299 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

Source-jamboree
[Reveal] Spoiler: OA

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Last edited by Bunuel on 16 Aug 2012, 23:12, edited 1 time in total.
Edited the question.
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Re: Sammy has flavors of candies with which to make goody bags [#permalink] New post 16 Aug 2012, 23:32
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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.

Answer: D.

Hope it's clear.
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Re: Sammy has flavors of candies with which to make goody bags [#permalink] New post 17 Aug 2012, 01:17
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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?
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Re: Sammy has flavors of candies with which to make goody bags [#permalink] New post 17 Aug 2012, 01:30
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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?


This is explained here: how-many-different-5-person-teams-can-be-formed-from-a-group-96244.html#p741834 and here: how-many-different-5-person-teams-can-be-formed-from-a-group-96244.html#p742026

Similar questions to practice:
a-certain-panel-is-to-be-composed-of-exactly-three-women-and-108964.html
a-box-contains-10-light-bulbs-fewer-than-half-of-which-are-99940.html
how-many-different-5-person-teams-can-be-formed-from-a-group-96244.html

Hope it helps.
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Re: Sammy has flavors of candies with which to make goody bags [#permalink] New post 30 Jun 2013, 23:46
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: Sammy has flavors of candies with which to make goody bags [#permalink] New post 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

Source-jamboree


OK, let me try this one

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.

Suff

Statement 2

Rearranging x-y = 17

We have the total

Suff

Answer is D

Hope it helps

Cheers!
J :)
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Re: Sammy has flavors of candies with which to make goody bags [#permalink] New post 25 May 2015, 06:57
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Re: Sammy has flavors of candies with which to make goody bags   [#permalink] 25 May 2015, 06:57
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