# 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

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