tricky probability

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?

Not that tricky, but the way people answer {(1/10) + (1/10)} doesn't show whether they have understood or not.

Sequence: P, S, T

Harry becoming secy: (9/10)*1/9 (not-harry becoming president, harry becoming secy) = 1/10

Harry becoming tresaurer = (9/10) (8/9) (1/8) = 1/10 ( harry not becoming P, not becoming S and becoming T)


Add 1/10 + 1/10 = 1/5