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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
1
7
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

66% (01:23) correct 34% (01:52) wrong based on 235 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

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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 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...
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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 Jan 2018, 08:27
goldfinchmonster wrote:
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...



Why are underwear and pants always referred to as a pair? Yes, there are two pant legs, but a shirt has two sleeves and nobody calls it a pair of shirts. — Apparelly Challenged, San Diego

Apparently so. “Pair,” from the Latin, means two like things. And pants (pantaloons) were originally two like things. You put them on one leg at a time because they actually came in two pieces. You put on one leg, tied it around your waist, then put on the other. From the beginning, about the 16th Century, pants have been referred to as a pair. Shirts were made from a single piece of cloth, so two sleeves didn’t inspire anybody to call them a pair of shirts. Or a pair of bras.
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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 14 Feb 2018, 20:31
When choosing the shirts, why do you use the combinatorics formula, as opposed to doing 8*7? My reasoning was 5 shoes * 3 pants * 3 jackets * 8 shirts * 7 shirts. Thank you
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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 12 Mar 2018, 09:56
can someone tell me why we use the combinations instead of permutations formula for the shirts? since on shirt is put on top of the other, only one can be seen, hence it matters which one is worn on top.
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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 12 Mar 2018, 18:10
I believe you have to use the combination formula because the order doesn't matter. For example:

say you have dresses 1,2,3,4,5,6,7, and 8. If you use permutation, you can choose dresses 7 and 5 but then in a separate situation you are saying that you can draw dresses 5 and 7. Both of these situations result in a similar group. Therefore, you have to use the combination formula to account for these repeating groups.
Re: Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jacke &nbs [#permalink] 12 Mar 2018, 18:10
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