Question

A man has 12 different colored shirts and 20 different ties in his closet. How many shirts and tie combinations can he select to take on a trip if he only takes 3 shirts and 5 ties?

Answer 1

The man can select 1,287,480 different shirt and tie combinations for his trip.

Step-by-step explanation:

To determine the number of shirt and tie combinations that the man can select for his trip, we can use the concept of permutations. Since he can choose 3 shirts out of 12 and 5 ties out of 20, we can calculate the number of combinations as:

Number of combinations = 12P3 * 20P5

Using the formula for permutations, this can be simplified to:

Number of combinations = (12! / (12-3)!) * (20! / (20-5)!)

After evaluating this expression, the number of shirt and tie combinations that the man can select for his trip is 1,287,480.