A committee of 11 members is to be formed from 8 males and 5 females.

Question

A committee of 11 members is to be formed from 8 males and 5 females. If $m$ is the number of ways the committee is formed with at least 6 males, and $n$ is the number of ways the committee is formed with at least 3 females, then:

Accepted Answer

At least 6 males means in the committee there can be 6 males or 7 males or 8 males.

$$ \therefore $$ m = $${}^8{C_6} \times {}^5{C_5} + {}^8{C_7} \times {}^5{C_4} + {}^8{C_8} \times {}^5{C_3}$$ = 78

At least 3 females means in the committee there can be 3 females or 4 females or 5 females.

$$ \therefore $$ n = $${}^5{C_3} \times {}^8{C_8} + {}^5{C_4} \times {}^8{C_7} + {}^5{C_5} \times {}^8{C_6}$$ = 78

So, m = n = 78

Solutions · 1