Question

A youth basketball coach has 12 kids on his team and he selects 5 kids to start each game. To be fair he wants to start a different group of 5 kids each game. How many different ways can he start 5 of the 12 players? If there is 20 games will he be able to start a different group of 5 kids for each game?

Answer 1

$_{12}C_5=\dfrac{12!}{5!7!}=\dfrac{8\cdot9\cdot10\cdot11\cdot12}{120}=792$

792>20, so yeah, he will be able.