A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes, in how many ways can the team be constituted?

Answer : There are 20 students in each classes and there is need of at least 5 students in each class to form a team of team of 11.

Now,

There are two ways in which the selection can be possible

1. Selecting 5 from XI and 6 from XII
2. Selecting 6 from XI and 5 from XII Now, considering first case,

No. of ways in selection of 5 students from 20 in class XI = ²⁰C5 No. of ways in selection of 6 students from 20 in class XII = ²⁰C6 By multiplication principle total no. of ways in first case is

= ²⁰C5      20C6

Now, considering second case,

No. of ways in selection of 6 students from 20 in class XI = ²⁰C6 No. of ways in selection of 5 students from 20 in class XII = ²⁰C5 By multiplication principle total no. of ways in second case is

= ²⁰C6 =20C5

Now the total no. of ways will be the addition of both the cases

= 20C5 X20C6 + 20C6 X20C5

= 2 x20C6 x20C5

Thus these are the ways by which A sports team of 11 students is to be constituted