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The Natural Woman, a women's health food store, offers its

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The Natural Woman, a women's health food store, offers its [#permalink]

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New post Updated on: 27 Aug 2014, 04:31
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The Natural Woman, a women's health food store, offers its own blends of trail mix. If the store uses 4 different ingredients, how many bins will it need to hold every possible blend, assuming that each blend must have at least two ingredients? (Also assume that each bin can hold one and only one blend.)

(A) 1
(B) 4
(C) 7
(D) 11
(E) 10
[Reveal] Spoiler: OA

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Originally posted by royQV on 27 Aug 2014, 01:31.
Last edited by Bunuel on 27 Aug 2014, 04:31, edited 1 time in total.
Renamed the topic and edited the question.
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Re: The Natural Woman, a women's health food store, offers its [#permalink]

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New post 27 Aug 2014, 04:34
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royQV wrote:
The Natural Woman, a women's health food store, offers its own blends of trail mix. If the store uses 4 different ingredients, how many bins will it need to hold every possible blend, assuming that each blend must have at least two ingredients? (Also assume that each bin can hold one and only one blend.)

(A) 1
(B) 4
(C) 7
(D) 11
(E) 10


The number of bins with 2 different ingredients = \(C^2_4=6\);
The number of bins with 3 different ingredients = \(C^3_4=4\);
The number of bins with 4 different ingredients = 1 (\(C^4_4=1\)).

The total number of bins with at least two ingredients = 6 + 4 + 1 = 11.

Answer: D.

Hope it's clear.
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Re: The Natural Woman, a women's health food store, offers its [#permalink]

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New post 17 May 2015, 14:02
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Hi All,

The answers to this question are relatively small, so if you don't see the "math" approach to solving this question, then you can 'brute force' the solution by "mapping out" all of the possibilities...

We're told that there are 4 ingredients (we'll call them A, B, C and D); we're told that each 'mix' must include AT LEAST 2 ingredients...

2 ingredient blends:
AB
AC
AD
BC
BD
CD

3 ingredient blends:
ABC
ABD
ACD
BCD

4 ingredient blends:
ABCD

Total blends = 6+4+1 = 11

Final Answer:
[Reveal] Spoiler:
D


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Re: The Natural Woman, a women's health food store, offers its [#permalink]

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New post 20 Nov 2017, 04:31
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Re: The Natural Woman, a women's health food store, offers its   [#permalink] 20 Nov 2017, 04:31
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