Question

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

Answer 1

Answer:

1. 19C8 = 75582

2. 19P8= 3047466240

Step-by-step 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.