man chooses clothing question

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slortta: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Sat Jan 23, 2010 8:13 am

by slortta » Thu Mar 25, 2010 12:47 am

A man chooses an outfit from 3 different shirts, 2 different pairs of shoes, and 3 different pants. If he randomly selects 1 shirt, 1 pair of shoes, and 1 pair of pants each morning for 3 days, what is the probability that he wears the same pair of shoes each day, but that no other piece of clothing is repeated?

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Source: Beat The GMAT — Problem Solving | Thu Mar 25, 2010 12:47 am

eaakbari: Master | Next Rank: 500 Posts; Posts: 435; Joined: Mon Mar 15, 2010 6:15 amFollowed by: 1 member; Thanked: 32 times

by eaakbari » Thu Mar 25, 2010 12:00 pm

Please do give the answer.

According to me it is 25/36

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analyst218: Master | Next Rank: 500 Posts; Posts: 140; Joined: Fri Feb 05, 2010 2:43 pm; Thanked: 3 times; GMAT Score:720

by analyst218 » Thu Mar 25, 2010 12:27 pm

slortta wrote:A man chooses an outfit from 3 different shirts, 2 different pairs of shoes, and 3 different pants. If he randomly selects 1 shirt, 1 pair of shoes, and 1 pair of pants each morning for 3 days, what is the probability that he wears the same pair of shoes each day, but that no other piece of clothing is repeated?

23/54

he will have 3x2x3 = 18 choices everyday.
since he can't repeat shirt and pants and have only 1 choice of shoes after the first day.
1st day: 3x2x3
2nd day: 2x1x2
3rd day: 1x1x1
--------
23 choices
OA please

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godspeed: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Sat Nov 28, 2009 11:21 am; Location: London

by godspeed » Thu Mar 25, 2010 5:56 pm

Yup 23/54.

[(3c1*2c1*3c1)+(2c1*1*2c)+(1c1*1*1c1)]/[(3c1*2c1*3c1)*3]

Pls post OA

~GS

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