Question

1. A coach writes the batting order of his starting 9 out of the team of 20 on a piece of paper. How many different ways could the list be written?

Answer 1

$N=20 \\ n=9 \\ Number \;of \;ways = \frac{N!}{n!(N-n)!} \\ = \frac{20!}{9!(20-9)!} \\ = \frac{12 \times 13 \times 14 \times 15 \times 16 \times 17 \times 18 \times 19 \times 20}{2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 9} \\ = 167960$