Question

Juan owns 7 pairs of pants, 3 shirts, 5 ties, and 6 jackets. How many different outfits can he wear to school if he must wear one of each item?

Answer 1

To solve this problem, just use multiplication.

`7\text{ pairs of pants}*3\text{ shirts}*5\text{ ties}*6\text{ jackets}=\large\boxed{630\text{ outfits}}`

You can somewhat think of this situation as a sort of tree. You start with 7 large branches representing the pants, then for every one of those you have 3 medium-sized branches to represent the pairs of pants. Each one of those has 5 sticks for the ties, which in turn each have 6 leaves to represent the jackets and therefore a complete outfit. The solution is found by getting the total number of leaves on the tree.