Answer to Question #293918 in Discrete Mathematics for Tege

Question

In how many ways can a committee of 5 teachers and 4 students be chosen from 9 teachers and 15 students ?

Answer 1

The 4 students can be chosen out of 15 in $^{15}C_4=\binom{15}{4}={15\times 14\times13\times12\over4\times3\times2}=1365$ ways.

The 5 teachers can be chosen out of 9 in $^{9}C_5=\binom{9}{5}={9\times 8\times7\times7\times6\over4\times3\times2}=126$ ways.

Hence, the committee can be formed in $1365\times126=171990$ ways.