Permutations and Computations help

rickrossticle1213 said:

Hi all, I have this three part problem that's really got me stumped, below is the problem. Any help would be greatly appreciated!
A club consists of 15 people including Amy, Dan, Jake, Josh, Jared, Zachary, Sara, and Steve. From the 15 members a president, vice president and treasurer will be selected at random. An advisory committee of 5 other individuals will then be selected at random.
a. Determine the probability that 3 of the 8 individuals named are selected for the three officers positions.
b. Assuming that 3 of the 8 individuals named are selected for the officers positions, determine the probability that the other 5 are selected for the advisory board.
c. Determine the probability that 3 of the 8 individuals named are selected for the three officers positions and that the other 5 are selected for the advisory board.

Now for part a. I've come up with ( ₈P₃ / ₁₅P₃ ) x ( ₅C₅ / ₁₂C₅ )= 1/6435... if my calculations and use of formulas is correct, i think I've got this one right, however i'm unsure of how to go about completing b and c. Any help or insight on how to go about finishing up this problem would really be appreciated!

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pka said:

I have tried to post corrections to this. each time I get a server error. What is going on.

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rickrossticle1213 said:

I had problems posting this problem myself, it became very frustrating. is it possible to post a solution in a word document then attach it to a post? I've become just short of fried from grilling over how to solve part's b and c.

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pka said:

This has nothing to do with me whatsoever. Here is a plain text file. To understand it one needs to know LaTeX.

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For part c you need \(\displaystyle \mathcal P \left({A \cap B}\right) = \mathcal P \left({A|B}\right) \; \mathcal P \left({A}\right)\)

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