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27 Jun 2008, 09:55
Kudos
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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
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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27 Jun 2008, 10:24
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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
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
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
