Question

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

Answer 1

Answer:

1. 75582

2. 3047466240

Step-by-step 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

$_nC_r = \frac{n!}{r!(n-r)!}$

$_19C_8=\frac{19!}{8!(19-8)!} = \frac{19!}{8!11!}=75582$

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

$_nP_r=\frac{n!}{(n-r)!} \\ _{19}P_8=\frac{19!}{(19-8)!} = 3047466240$