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

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Senior Manager
Joined: 14 Aug 2006
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A man chooses an outfit from 3 different shirts, 2 different [#permalink]  07 Sep 2006, 08:08
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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 * (1/2)^3
B. (1/3)^6 * 1/2
C 1/3 ^ 4
D (1/2) ^2 * 1/2
E 5 * (1/3)^2
CEO
Joined: 20 Nov 2005
Posts: 2913
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
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C

Day1 - He can choose anything. Prob = 1
Day2 - He has 2 shirts he can use out of total 3 shirts , 1 out of 2 shoes and 2 out of 3 pants. = 2/3 * 1/2 * 2/3
Day3 - He has 1 shirts he can use out of total 3 shirts , 1 out of 2 shoes and 1 out of 3 pants. = 1/3 * 1/2 * 1/3

Total = 1 * 2/3 * 1/2 * 2/3 * 1/3 * 1/2 * 1/3 = (1/3)^4
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

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How does this assure us that the same pair of shoes are worn on all the three days?

Thanks/

ps_dahiya wrote:
C

Day1 - He can choose anything. Prob = 1
Day2 - He has 2 shirts he can use out of total 3 shirts , 1 out of 2 shoes and 2 out of 3 pants. = 2/3 * 1/2 * 2/3
Day3 - He has 1 shirts he can use out of total 3 shirts , 1 out of 2 shoes and 1 out of 3 pants. = 1/3 * 1/2 * 1/3

Total = 1 * 2/3 * 1/2 * 2/3 * 1/3 * 1/2 * 1/3 = (1/3)^4
CEO
Joined: 20 Nov 2005
Posts: 2913
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 18

Kudos [?]: 121 [0], given: 0

haas_mba07 wrote:
How does this assure us that the same pair of shoes are worn on all the three days?

Thanks/

ps_dahiya wrote:
C

Day1 - He can choose anything. Prob = 1
Day2 - He has 2 shirts he can use out of total 3 shirts , 1 out of 2 shoes and 2 out of 3 pants. = 2/3 * 1/2 * 2/3
Day3 - He has 1 shirts he can use out of total 3 shirts , 1 out of 2 shoes and 1 out of 3 pants. = 1/3 * 1/2 * 1/3

Total = 1 * 2/3 * 1/2 * 2/3 * 1/3 * 1/2 * 1/3 = (1/3)^4

Say he wore PAIR#1 on day 1.
Prob of choosing PAIR#1 on day2 is 1/2.
Prob of choosing PAIR#1 on day3 is 1/2.
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

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Another way to to this is:

On Day 1 the following is possible:

3 possible shirt choices * 2 possible shoe choices * 3 possible pant choices = 18

On Day 2:

2 possible shirt choices * 1 possible shoe choice * 2 possible pant choies
= 4

On Day 3:

1 possible shirt choice * 1 possible shoe choice * 1 possible pant choice
= 1

We also know that total possible choices are 3*3*2 = 18

So

From the different days we get 18/18 * 4/18 * 1/18 = 1/1 * 2/9 * 1/18
= 4/324 = 1/81 = (1/3)^4
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