Three sides of a regular polygon with 8 sides are chosen at random. Find the probability that, when these sides are extended, they form a triangle containing th
Mathematics
sttblack
Question
Three sides of a regular polygon with 8 sides are chosen at random. Find the probability that, when these sides are extended, they form a triangle containing the polygon.
1 Answer

1. User Answers konrad509
[tex]\Omega={8\choose 3}=\dfrac{8!}{3!5!}=\dfrac{6\cdot7\cdot8}{6}=7\cdot8=56[/tex]
There are two possibilities of choosing three sides of the polygon, so when they are extended, they form a triangle containing the polygon (pictures in the attachment). Multiplying it by the number of sides, gives us 16 possibilities in total.
[tex]A=16\\\\ P(A)=\dfrac{A}{\Omega}\\ P(A)=\dfrac{16}{56}=\dfrac{2}{7}[/tex]