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Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jacke

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Director
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Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jacke [#permalink]

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New post 28 Nov 2010, 05:54
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Difficulty:

  35% (medium)

Question Stats:

72% (02:21) correct 28% (01:47) wrong based on 58 sessions

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Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jackets for her business trip. If an outfit consists of one of each item of clothing except shirts, of which she will wear 2, how many different outfits can does Grace have available during her trip?

(A) 2,520
(B) 1,260
(C) 620
(D) 360
(E) 120
[Reveal] Spoiler: OA

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Re: Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jacke [#permalink]

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New post 28 Nov 2010, 08:54
The idea is to multiply the number of possibilities for each item of clothing with the different items. For the shirts you essentially choose 2 out of 8 so you should use the combination forumla (don't know how to use math symbols here).

This gives you 5 x 3 x 28 x 3 = 1'260. Hence, solution B is correct.
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Re: Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jacke [#permalink]

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New post 28 Nov 2010, 20:38
5*3*(8!/2!((8-2)!)*3 = 5*3*28*3= 1260

answer is B.
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Re: Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jacke [#permalink]

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New post 28 Nov 2010, 23:13
5*3*(8!/2!((8-2)!)*3 = 5*3*28*3= 1260
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Re: Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jacke [#permalink]

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New post 13 Nov 2015, 03:30
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Re: Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jacke [#permalink]

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New post 13 Nov 2015, 09:53
Hey can anyone explain me why 3 pair of pants does not signifies a total of 6 units of pants.

I agree that a pair of socks or shoes can be counted as single unit as they are worn in pair, but how in case of pants, pants can't be worn in pairs in general case.

Will be nice if some one can explain this query...
Re: Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jacke   [#permalink] 13 Nov 2015, 09:53
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Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jacke

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