Question

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 ?

Answer 1

Total number of students is XI = 20

Total number of students is XII = 20

Total number of students to be selected in c team = 11

(at least 5 from XI and 5 from XII)

this can be done in following ways

${}^{20}{C}_5{\times }^{20}{C}_6{+}^{20}{C}_6{\times }^{20}{C}_5=2{(}^{20}{C}_6{\times }^{20}{C}_5)=(\frac{20!}{6!14!}\times \frac{20!}{5!15!})=\frac{2\times 20\times 19\times 18\times 17\times 16\times 15\times 20\times 19\times 18\times 17\times 16}{6\times 5\times 4\times 3\times 2\times 5\times 4\times 3\times 2\times 1}=19\times 17\times 16\times 15\times 2\times 19\times 3\times 17\times 8$
= 120 1870080 ways