**Question:**

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

**Solution:**

We know that,

nCr

$=\frac{n !}{r !(n-r) !}$

A team of 11 students can be constituted in the following two ways

(i) 5 students from class XI and 6 students from XII = 20C5. 20C6

(ii) 6 students from class XI and 5 students from XII = 20C6.20C5

The number ways the team can be constituted = Case(i)+case(ii)

= 20C5. 20C6 + 20C6.20C5

= 2(20C5. 20C6)