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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) # The Natural Woman, a women's health food store, offers its  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Manager Joined: 24 Apr 2012 Posts: 50 Concentration: Strategy WE: Project Management (Consulting) The Natural Woman, a women's health food store, offers its [#permalink] ### Show Tags Updated on: 27 Aug 2014, 03:31 2 00:00 Difficulty: 25% (medium) Question Stats: 79% (01:45) correct 21% (01:58) wrong based on 150 sessions ### HideShow timer Statistics 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 will to win, the desire to succeed, the urge to reach your full potential..." Useful Links: http://gmatclub.com/forum/powerscore-cr-notes-hope-that-someone-find-it-kudosofiable-174638.html#p1384561 Originally posted by royQV on 27 Aug 2014, 00:31. Last edited by Bunuel on 27 Aug 2014, 03:31, edited 1 time in total. Renamed the topic and edited the question. Math Expert Joined: 02 Sep 2009 Posts: 50578 Re: The Natural Woman, a women's health food store, offers its [#permalink] ### Show Tags 27 Aug 2014, 03:34 4 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. _________________ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12853 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The Natural Woman, a women's health food store, offers its [#permalink] ### Show Tags 17 May 2015, 13:02 1 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: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Joined: 21 May 2018
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Re: The Natural Woman, a women's health food store, offers its  [#permalink]

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30 May 2018, 06:59
Can I ask why the following is wrong?

Total possible blends = 4! = 24
Blends with 1 ingredient = 4!/3! = 4
Blends with 2 or more ingredients = 24-4 = 20

Why is the answer 11 and not 20? I understand the method of adding up blends with 2,3,4 ingredients, but why is my method wrong?

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

### Show Tags

30 May 2018, 11:54
1
Hi strawberrycupcake,

Your first calculation (4!) is the total number of ways to ARRANGE ALL 4 ingredients (meaning that all 4 are used). However, that is not what the question asks us for - it's asking for the number of combinations of AT LEAST 2 of the ingredients.

Besides using 'brute force' to just list out all of the possibilities, you could use the Combination Formula 3 times and then add up the individual results:

4c2 + 4c3 + 4c4 = 6 + 4 + 1 = 11

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
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Re: The Natural Woman, a women's health food store, offers its &nbs [#permalink] 30 May 2018, 11:54
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