probability

[sunilrawat]

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?


OA later

[Frankenstein]

Hi,
Favorable case:
Day1 : shirt can be selected in 3 ways, shoe in 2ways, pant in 3 ways -->3*2*3
Day2 : shirt can be selected in 2 ways, shoe in 1 way, pant in 2 ways -->2*1*2
Day1 : shirt can be selected in 1 way, shoe in 1 way, pant in 1 ways -->1*1*1
Total outcomes = 3^2.2^3

All possible cases:
Day1 : shirt can be selected in 3 ways, shoe in 2ways, pant in 3 ways
Day2 : shirt can be selected in 3 ways, shoe in 2ways, pant in 3 ways
Day3 : shirt can be selected in 3 ways, shoe in 2ways, pant in 3 ways
Total outcomes = 3^3.2^3.3^3

Hence, probability is 3^2.2^3/3^3.2^3.3^3 = 1/3^4

[sunilrawat]

OA 1/3^4

my approach was same. I made a silly calc mistake.