k! ----------------- n! (k-n)!where k! (pronounced "k factorial") is 1*2*3*...*k. To compute an easy example, if you had a lottery with 6 numbers and you had to choose 3 of them to win, the number of possible combinations would be:

6! ---------------- 3! (6-3)! or 1 * 2 * 3 * 4 * 5 * 6 ---------------------------------- (1 * 2 * 3) (1 * 2 * 3) or 4 * 5 * 6 ----------------------- 6 which is 20.Oddly enough this ties into Pascal's Triangle:

1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 etc.To find the number of ways you can choose 3 objects out of 6, you first count down to row 6 (noting that the first row is 0) and then count across to column 3 (again remembering that the first column is 0). Sure enough you get 20 again. Pretty hip huh? :)

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