Combinations Probability Problem

cmkluza said:

Hello, I apologize for the vagueness of the title, but I'm not sure how to describe this problem efficiently, and well. The problem statement is as follows:

A room has nine desks arranged in three rows of three desks. Three students sit in the room. If the students randomly choose a desk find the probability that two out of the three front desks are chosen.

I'm not too sure where to begin. I'd imagine that this is a combination question, so would I try to get all possible combinations, meaning 9 pick 3, and then just find the combinations with two in the front two desks and make a probability out of those numbers? So, would I go with 3 pick 2, for a sum total of 3/84? I can't figure out what to do with this question, so any assistance will be greatly appreciated.

Thanks!

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Jomo said:

Hi, You almost have it. This type of problem is called hypergeometic.
You 1st have to pick 2 from 3 and then (that means to multiply) pick 1 from 6 and divide this result by 9 pick 3.
So the answer is 3C2*6C1/9C3= 3*6/84=3/14. Why did you think that you can pick the last seat in exactly one way?

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cmkluza said:

Thanks for your response! I think I'm starting to understand this problem. So you're picking two out of the three front seats, and then you just need to pick one from the remaining six seats. Perhaps if I wasn't so tired I could understand, but why is it that you multiple the possible ways to pick two from the front three seats with the possible ways you pick one from the back six seats? I think I'm missing a large part of the basis for this subject, so I guess I'll be studying it a lot more to make sense of it all.

Thank you very much for your help!

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