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. 75582

2. 3047466240

Explanation:

1. If order does not matter, this is a combination problem. You are choosing 8 sticks from a set of 19. (Octagons have 8 sides.)

The formula for combinations of n things chosen r at a time "n choose r" is

`_nC_r = (n!)/(r!(n-r)!)`

`_19C_8=(19!)/(8!(19-8)!) = (19!)/(8!11!)=75582`

2. If order matters, there are more possibilities. This is a permutation problem. The number of permutations of 19 things taken 8 at a time, "19 permute 8" is

`_nP_r=(n!)/((n-r)!) \\ _(19)P_8=(19!)/((19-8)!) = 3047466240`