A man has 5 sport coats 4 pairs of slacks 6 shirts and 1 tie

A man has 5 sport coats, 4 pairs of slacks, 6 shirts, and 1 tie. How many combinations of these can he wear, if he must wear at least slacks and a shirt?

Solution

number of combinations = 2^5 * (2^4 -1) * (2^6-1) *2^1= 60480

explaination : from 5 sport coats , we can select in 2^5 ways since each coat has two options (either selected, or left out)

similarly from 4 pair of socks, we can select in 2^4 -1 ways (same explaination as above but there should be atleast 1 pair of socks .i.e we must remove the case where no socks is selected)