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Probability

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by BTGmoderatorRO » Sun Dec 24, 2017 8:40 am
A certain club has 10 members, including Harry. One of the 10 members is 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 chose to be secretary or the member chose to be treasurer?

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

OA is E

Can an Expert reveal the best method to solve this question of Probability? Thanks
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by elias.latour.apex » Sun Dec 24, 2017 10:34 am
There are a number of ways to solve this problem. Here's one approach:

There are 10x9x8 ways that people can be picked to fill the three roles, i.e. 720. The question is: How many ways can Henry be chosen to be secretary and how many ways can he be chosen to be treasurer?

If Henry is Treasurer, there are 9 people who could fill the president spot, and 8 remaining people who could be secretary for a total of 72 possibilities.
If Henry is Secretary, there are 9 people who could fill the president spot, and 8 remaining people who could be treasurer for a total of 72 possibilities.

So Henry's chance of being in one of the roles is 2(72)/720, which reduces to 2/10 or 1/5.
Elias Latour
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