Tuesday, January 22, 2008

Simplifying with Factorials

As I was grading the second quiz, I see that I should point out that you should simplify as much as possible whenever you see a fraction involving factorials. For example suppose that you saw a fraction: 10!/(4!6!). You should know that immediately you can cancel the last 6 numbers to get: (10*9*8*7)/(4*3*2*1). But instead of multiplying out, you should cancel the 8 with 4*2 and the 9 with 3 to get: (10*3*7)=210.
If you just multiply things out and do not simplify as you go, you will find that you get some awful numbers that are hard to find factors. In fact, you probably already were looking at the factors.

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