Question

A group of 22 7th grade girls is to be divided into a varsity team and a junior varsity team of 11 each. How many different divisions are possible?

Answer 1

Answer:

705,432 ways

Step-by-step explanation:

Since no girl will be left out once both teams are selected when selecting the varsity team, the junior varsity team is automatically composed by the players not selected, the number of ways to select both teams is:

$n = \frac{22!}{(22-11)!11!} \\n=705,432$

There are 705,432 ways to divide the girls into a varsity team and a junior varsity team.