Question

A sports team of 11 students is to be constituted choosing at least 5 from class IX and at least 5 from class X. If there are 8 students in each of these classes, in how many ways can the team be constituted?

Answer 1

$11$ Students

Atleast $5$ from $9th$ class

$5$ from $10th$ class

$8$ in each class

the $11th$ member can be $9th$ or $10th$ class

$\Rightarrow \left[{}^8{C}_6{\ast }^8{C}_5\right]\times 2\Rightarrow \frac{8\times 7}{2}\times 56\times 2\Rightarrow 3136$

Hence the correct answer is $3136$ Ways