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help with probability

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by allenkt » Fri Apr 20, 2007 6:03 pm
For some reason I really seem to struggle with probability questions. Here is one that was on my GMATPrep that I just can't figure out. It seems like its relatively but something just isn't clicking. Here is the question (as best I remember it but the numbers are correct):

There are 10 students in a class and they are going to pair off in groups of 2. How many different combinations are possible? The answer is 45 but I don't know how they got there. I think it would have something to do with factorials but I don't know.
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Source: — Quantitative Reasoning |
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by allenkt » Fri Apr 20, 2007 6:10 pm
I probably should just delete my last post but in case someone else is struggling with this I wanted to give the solution. As soon as I wrote out the problem and realized it would involve factorials I vaguely remembered a formula I had seen. Once I found it and plugged it in it provided the solution.

The formula is C(n,r) = n! / r! (n-r)!

So solving for C(10,2) = 10! / 2! (10-2)! which simplifies down to 9 x 5 / 1 and that equals 45.

Hopefully I'll remember this during the test....
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