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# A man chooses an outfit from 3 different shirts, 2 different

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Manager
Joined: 09 May 2006
Posts: 99
Location: Bangalore, India
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A man chooses an outfit from 3 different shirts, 2 different [#permalink]  11 Jun 2006, 00:22
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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?
Intern
Joined: 06 May 2006
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Re: PS - Probability [#permalink]  11 Jun 2006, 00:45
On the first day the man has a total of 3 x 2 x 3 = 18 combinations to choose from.

when he gets to the next day he has 1shoes x 2 shirts x 2 pants = 4 choices in order not to repeat any of the shirts and pants and also to keep the same shoes. hence a total probability for this event is 4 / 18

on the third day there is only 1 choice remaining so that he does not repeat any of the shirts and pants of the other two days and keeps the same shoes. hence the total probability of this event is 1 / 18

in order for this to happe consecutively on the 2nd and 3rd day the probability for that to happen is 4/18 x 1/18 = 1/81
Senior Manager
Joined: 09 Mar 2006
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(2/3)*(1/3) * (2/3)*(1/3) * (1/2)*(1/2) = 1/81
---(shirts)-------(pants)-------(shoes)-----(total)---
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