Question

A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the treasurer?

(A) 1/720
(B) 1/80
(C) 1/10
(D) 1/9
(E) 1/5

Answer 1

(E) 1/5

Explanation:

The probability that Harry will be chosen to be the secretary but not the president is
`(9)/(10) *(1)/(9) =(1)/(10)`

The probability that Harry will be chosen to be the treasurer but not the president or secretary is
`(9)/(10) *(8)/(9)*(1)/(8)=(1)/(10)`

Thus, the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the treasurer is
`(1)/(10) + (1)/(10) = (1)/(5)`