Probability question w/ exponents

[undvaulter]

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(1/3)^2

[ps63739]

Let's take day by day -

Day 1 (favourable outcome) - He can select shoes two ways, Shirts and Pants each 3 ways = 2*3*3.
Total number of outcomes = 2*3*3
So P(Day1) = 2*3*3/2*3*3 = 1
Day 2 (Favourable outcomes) - He can select shoes 1 (he has to wear the same shoe) way and select the pants and shirts 2 ways each (as he cannot wear the Shirt and Pant he wore Day1) = 1*2*2
Total outcomes = 2*3*3

So P(Day2) = 1*2*2/2*3*3 = 2/9.
Day 3 - in the similar fashion
P(day3) = 1/18

Now probability here will be multiplied.

Total probability will be = P(Day1) happens and P(Day2) happens and P(Day3) happnes.

That gives P= 1*(2/9)*(1/18)
= 1/3^4.

[Ben Ku]

Please cite the source (author) of this problem. We cannot reply unless a source is cited (and, if no source is cited, we will have to delete the post!). Thanks.

[shalinibhatia15]

hi this is from gmatprep

Please cite the source (author) of this problem. We cannot reply unless a source is cited (and, if no source is cited, we will have to delete the post!). Thanks.

[mschwrtz]

Thanks, we'll move it over to that forum.