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)