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Probability question

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Junior | Next Rank: 30 Posts
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Joined: Mon Jul 23, 2007 7:39 am

Probability question

by shymab » Sun Aug 19, 2007 8:09 pm
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?

A. (1/3)^0 (1/2)^3
B. (1/3)^0 (1/2)
C. (1/3)^4
D. (1/3)^2 (1/2)
E. 5(1/3)^2

Answer is C. How?
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Master | Next Rank: 500 Posts
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by beny » Sun Aug 19, 2007 11:00 pm
The first day, he can choose any shirt, any shoes and any pants:

Probability = 1

The second day, he can choose from 2 shirts, 2 pants, and must wear the same shoes:

2/3 * 2/3 * 1/2

The third day, he must wear the unworn shirt, unworn pants, and same shoes:

1/3 * 1/3 * 1/2

Althogether:

1 * 2/3 * 2/3 * 1/2 * 1/3 * 1/3 * 1/2
= 1/3 * 1/3 * 1/3 * 1/3
= (1/3)^4
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Junior | Next Rank: 30 Posts
Posts: 11
Joined: Mon Jul 23, 2007 7:39 am

Thank you

by shymab » Mon Aug 20, 2007 9:46 pm
Thank you. That was clear. Probability and permutations are still murky topics for me. Any suggestions on how I can improve my skills in these topics will be appreciated.
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