A committee of six is to be formed by a state governor from nine state commissioners and three members of the state house of assembly. In how many ways can the members of the committee be chosen so as to include one member of the house of assembly
-
A.
378 ways -
B.
462 ways -
C.
840 ways -
D.
924 ways
Correct Answer: Option A
Explanation
(^{3}C_{1} times ^{9}C_{5}=frac{3!}{(3-1)!1!}times frac{9!}{(9-5)!5!}\=frac{3!}{2!1!}times frac{9!}{4!5!}\=frac{3 times 2!}{2!times 1}times frac{9times8times7times6times5!}{4times3times2times1times5!}\=3times9times2times7\=378 hspace{1mm}ways)