Answer to Question #117117 in Combinatorics | Number Theory for Priya

Question

A man has 3 different suits, 4 different shirts and 5 different pairs of shoes. In how many different ways can this man wear a suit, a shirt and a pair of shoes?

Answer 1

The man has 3 different suits, 4 different shirts and 5 different pairs of shoes.

So, the different number of ways he can choose a suit = 3C1 = 3, where nCr is the combination of r different things from n different things.

The different number of ways he can choose a shirt = 4C1 = 4

The different number of ways he can choose a pair of shoes = 5C1 = 5

Therefore, the total number of ways the man can wear a suit, a shirt and a pair of shoes = 3 X 4 X 5 = 60

Answer: The man can wear a suit, a shirt and a pair of shoes in 60 different ways.