Answer:
1. 75,582 ways
2. 3,047,466,240 ways
Step-by-step explanation:
1-An octagon is an 8-sided polygon.
-A combination is an arrangement of a sequence without any defined order. Order doesn't matter
-Given that there are 19 sticks, the combination to form octagons can be calculated as:
[tex](\limits^n_k)=\frac{n!}{k!(n-k)!}\\\\(\limits^{19}_8)=\frac{19!}{8!(19-8)!}\\\\=75,582\ ways[/tex]
Hence, there are 75,582 ways to arrange the sequence in nor particular order.
2. This question tests our knowledge of permutations.
-A permutation is an arrangement of a set's elements in a defined order.
-Permutation is given by the formula:
[tex]P(n,r)=\frac{n!}{(n-r)!}, \ \ \ n=19, r=8\\\\P(19,8)=\frac{19!}{(19-8)!}\\\\=3047466240 \ \ ways[/tex]
Hence, there are 3,047,466,240 ways to make an octagon from 19 sticks in an ordered manner.
