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

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Director
Joined: 07 Jun 2004
Posts: 589
Location: PA
Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jacke  [#permalink]

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28 Nov 2010, 04:54
1
7
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Difficulty:

45% (medium)

Question Stats:

64% (01:58) correct 36% (02:14) wrong based on 236 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
Manager
Joined: 02 Apr 2010
Posts: 99
Re: Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jacke  [#permalink]

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28 Nov 2010, 07:54
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.
Manager
Joined: 13 Jul 2010
Posts: 130
Re: Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jacke  [#permalink]

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28 Nov 2010, 19:38
5*3*(8!/2!((8-2)!)*3 = 5*3*28*3= 1260

Manager
Joined: 13 Apr 2015
Posts: 74
Concentration: General Management, Strategy
GMAT 1: 620 Q47 V28
GPA: 3.25
WE: Project Management (Energy and Utilities)
Re: Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jacke  [#permalink]

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13 Nov 2015, 08:53
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...
Intern
Joined: 30 Oct 2017
Posts: 9
Re: Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jacke  [#permalink]

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28 Jan 2018, 07:27
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.
Intern
Joined: 19 Jun 2017
Posts: 1
Re: Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jacke  [#permalink]

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14 Feb 2018, 19:31
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
Intern
Joined: 28 Feb 2018
Posts: 2
Re: Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jacke  [#permalink]

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12 Mar 2018, 08:56
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.
Intern
Joined: 04 Jan 2018
Posts: 4
Location: United States
GMAT 1: 700 Q47 V39
GPA: 3.34
WE: Military Officer (Military & Defense)
Re: Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jacke  [#permalink]

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12 Mar 2018, 17:10
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   [#permalink] 12 Mar 2018, 17:10
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