hi
I am preparing for GMAT and came across a question for which I had no answer. Can you please publish the question so that I can discuss about it in you forum? The question is described below:
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?
(1)(1/3)pow6(1/2)pow3
(2)(1/3)pow6(1/2)
(3)(1/3)pow4
(4)(1/3)pow2(1/2)
(5)5X(1/3)pow2
N.B: pow = power
Authors bio is coming up shortly. 
I can´t find the answer above.
My answer would be:
Multiplication of the following:
shoes: 1/2 X 1/2
shirt: 2/3 X 1/3
pants 2/3 X 1/3
therefore:
(1/2)pow2(1/3)pow2(2/3)pow2
here is the solution,
Selection of pair of shoes:
On first day, any pair of shoes can be selected out of two pair
Probability will be: 2/2
As second day he has to wear same pair of shoes so pobability of selceting same pair of shoes will be: 1/2
Same way, probability of selecting same pair of shoes will be: 1/2
So net probability of wearing same pair of shoes all three days will be: 2/2 x 1/2 x 1/2 = 1/4
Same way:
Any shirt can be selected for first day, so probability will be: 3/3
For second day we have only only two shirts to select from 3, so probability of not selecting the first day shirt will be: 2/3
For third, we are left over with only one shirt which is not used, so probability will be: 1/3
Net probability of wearing different shirts all three days: 3/3 x 2/3 x 1/3 = 2/9
Same way, probability of wearing different pants in all three days will be: 3/3 x 2/3 x 1/3 = 2/9
So final net probability is: 1/4 x 2/9 x 2/9 = 1/81 = (1/3) pow 4
Is this answers your question?
Regards,
Husain
Ans: (3)
i also think the same, the solution will be same as stated by Husain.
The answer is option 3.
The probability of choosing the shirt for 3 days is 1/3*2/3*1/1=2/9 which is same for pants also.
For shoe the probability is (1/2*1/2*1/2)*2 as there are 2 pairs of shoes.
Hence ,probability is 2/9*2/9*1/4=(1/3)pow4
I agree Hussain
Ans should be 3
3