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Difficulty:
85%
(hard)
Question Stats:
46% (02:02) correct
54%
(02:12)
wrong
based on 1134
sessions
History
Date
Time
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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).
(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
(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
17 Aug 2012, 00:32
Kudos
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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.
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.
General Discussion
17 Aug 2012, 02:17
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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?
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?
