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
[tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex]
[tex]_19C_8=\frac{19!}{8!(19-8)!} = \frac{19!}{8!11!}=75582[/tex]
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
[tex]_nP_r=\frac{n!}{(n-r)!} \\ _{19}P_8=\frac{19!}{(19-8)!} = 3047466240[/tex]
