Question

Jen's favorite band is going on tour this summer. There are eight different concert dates that Jen could attend. She can only afford to see three shows. How many possible combinations are available for Jen?

Answer 1

The number of possible combinations can be calculated by formula $C_n^k= \frac{n!}{k!(n-k)!}$.

There are eight different concert dates that Jen could attend, then n=8.

Jen can only afford to see three shows, then k=3

and


$C_8^3= \frac{8!}{3!(8-3)!}=\frac{1\cdot 2\cdot 3\cdot 4\cdot5 \cdot 6\cdot 7\cdot 8}{1\cdot 2\cdot 3\cdot 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5} =56$

Answer: 56 possible combinations.