Question

1. How many ways are there to make an octagon with 19 different sticks when order DOESN’T matter?

2. How many ways are there to make an octagon with 19 different sticks when order MATTERS?

Answer 1

1. 19C8 = 75582

2. 19P8= 3047466240

Explanation:

First, find the number of ways to get 8 sticks from 19. At first, you have 19 choices, then 18, then 17, all the way to 12. Giving you 19*18*17*...*13*12, or 19!/11!.

Combination:

When order doesn't matter, you have to divide 19!/11! by the number of ways to order 8 sides, or 19!/11!/8!=19C8=75582

Permutation:

When order doesn't matter, you don't have to divide 19!/11! by the number of ways to order 8 sides, since you count each of these, and 19!/11!=19P8=3047466240.