Question

How many ways can a committee chairman choose 4 people for a subcommittee if there are 12 members on the whole committee?

a. 48
b. 495
c. 11,880
d. 20,736

Answer 1

A group of k elements can be chosen from a group of n elements in
`(n!)/(k!(n-k)!)` ways.


`(^(12) _4)=(12!)/(4!(12-4)!)=(12!)/(4! * 8!)=(8! * 9 * 10 * 11 * 12)/(2 * 3 * 4 * 8!)=(9 * 10 * 11 * 12)/(2 * 3 * 4)= \\ \\ =3 * 5 * 11 * 3=495`

The answer is B. 495.