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

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Senior Manager
Joined: 31 Jul 2006
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A man chooses an outfit from 3 different shirts, 2 different [#permalink]  15 Oct 2006, 14:48
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?

(1/3)^6 * (1/2)^3

(1/3)^6 * (1/2)

(1/3)^4

(1/3)^2 * (1/2)

5*(1/3)^2
VP
Joined: 25 Jun 2006
Posts: 1175
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I got C.

Total # of possible dressings:
(3*2*3)^3 for 3 days.

Desired # of dressings:
shoes: 2 choices for 3 days: 2.
shirts for 3 days unrepeated: 3!
pants for 3 days unrepeated: 3!

so :

(2*3!*3!)/(3*2*3)^3 = C
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