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?

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 20C6 + 20C6 20C5


= 2 20C6 20C5


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


1