SOLUTION: 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

Algebra ->  Probability-and-statistics -> SOLUTION: 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      Log On


   

Question 1136123: 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 by ikleyn(52771) About Me  (Show Source):
You can put this solution on YOUR website!
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How many ordered triples can you form of 10 items ?

    10*9*8 = 720.



How many ordered triples can you form, where Harry occupies the #2 position ?

    Obviously, 9*8 = 72  

    (simply putting someone of remaining 9 persons to position #1 and someone of remaining 8 persons to position #3).



How many ordered triples can you form, where Harry occupies the #3 position ?

    Obviously, 9*8 = 72  

    (using same arguments).



So, your space of all events consists of 720 elements; of them, favorable are 72 + 72 = 144 events.


Therefore, the probability the problem asks for, is  144%2F720 = 1%2F5 = 2%2F10 = 0.2 = 20%.     ANSWER