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 teams be constituted?
Given that we need to choose a team of 11 students with at least 5 from class XI and 5 from class XII.
It is also mentioned that each class constitutes 20 students.
There are two cases of selecting a team:
i. 6 from class XI and 5 from class XII
ii. 5 from class XI and 6 from class XII
Let us assume the total no. of ways of selecting 11 students to be N.
⇒ N = no. of ways of selecting 11 students from both classes
⇒ N = (No. of ways of selecting 6 students from class XI and 5 students from class XII) + (No. of ways of selecting 5 students from class XI and 6 students from class XII)
⇒ N = (20C6 × 20C5) + (20C5 × 20C6)
We know that ,
And also n! = (n)(n – 1)......2.1
⇒
⇒
⇒
⇒ N = ((38760) × (15504)) + ((15504) × (38760))
⇒ N = 600935040 + 600935040
⇒ N = 1201870080 ways