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?​

Answer 1

Answer:

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

This question is much easier than it appears.

Each member out of 10, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/10 and the probability that Harry will be selected to be the treasurer is also 1/10. So, the probability that Harry will be selected to be either the secretary or the the treasurer is 1/10+1/10=2/10.

Answer: E.