From a pool of 12 seniors and 10 juniors, a team of 10 members is to be formed. How many distinct ways can the team be chosen if it must consist of exactly 5 seniors and 5 juniors?

Explanation

To form the group, select 5 seniors from 12, which can be done in 12C5 ways. Similarly, select 5 juniors from 10, which can be done in 10C5 ways. Therefore, the total number of ways to form the group is 12C5 × 10C5. Since 12C5 equals 12C7, the expression can also be written as 12C7 × 10C5.