Question

How many different outfits can you make with 3 pairs of shoes, 4 pairs of pants, 5 shirts and 2 hats?

Answer 1

3*4*5*2 = 120

Answer 2

This is just the application of Rule of product ( http://en.wikipedia.org/wiki/Rule_of_product) of combinatorics.

With every pair of shoes we can choose to wear any pants and any shirt and any hat so total number of ways of doing this will be

\[3 \times 4 \times 5 \times 2 = 5!=120 \]