Problem Solving

Hi,

I've got this:
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 reasurer. What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the reasurer?

First I wanted to to: 1/9 + 1/8 .. but it was too simple

I need to calculate:
1) 9/10 * 1/9 = 1/10
2) 9/10 * 1/9 * 1/8 = 1/10
1/10 + 1/10 = 1/5

For me it's a little bit unclear, why it is ok to compute 9/10 and 1/9 two times ..
Yes, ok .. because either secretary OR tresurer.

But how can I come to this conclusion on my own?
What should I write onto my flashcard now?
I would like to write a concept down to memorize it.
Could you give me a hint?

Thank you in advance.
Bye, Chris

P(SEC) = 9/10 * 1/9 = 1/10
P(TRES)= 9/10 * 8/9 * 1/8 = 1/10

1) probability that he is NOT PRESIDENT AND SECRETARY
2) probability that he is NOT PRESIDENT AND NOT SECRETARY AND TRES.

Probability of being SEC OR TRES = P(Sec) + P(Tres)
Hope that helps.