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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?
A. 1/ 3^6 x 1/2^3
B. 1/ 3^6 x 1/2
C. 1/ 3^4
D. 1/ 3^2 x 1/2
E. 5 x 1/ 3^2
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total number of ways the man can select his clothes on a day = 3*3*2 on 3 days = (3*3*2)^3
On day 1 number of ways shoes can be selected = 2 number of ways shirts can be selected = 3 number of ways pants can be selected = 3
on day 2 number of ways shoes can be selected = 1 (has to select the same pair of shoes) number of ways shirts can be selected = 2 (can not repeat the shirt) number of ways pants can be selected = 2 (can not repeat the pants)
On day 3 number of ways shoes can be selected = 1 (has to select the same pair of shoes) number of ways shirts can be selected = 1 (has to take the third shirt) number of ways pants can be selected = 1 (has to take the last pants)
Probability = (2*3*3)*(1*2*2)*(1*1*1) / (3*3*2)^3 = 1 / 3^4... option C
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