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Probability: Counting the Possibilities
If you have 3 books, there are 6 ways (3 x 2 x 1) to arrange them and with 4 books there are 24 ways (4 x 3 x 2 x 1) so with 10 books there are 10! (10 factorial: 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) or 3,628,800 ways. This is the Fundamental Principle of Counting
If we were to choose 2 students to be president and vice presdent from a class of 10, there would be 90 possibilities using a permutation (first choose from 10 then after you pick that person there are 9 left). If, however, you would like teams of two without ranking (no Pres and VP), there would be half that number -- 45 combinations. We can use nPr and nCr on the Texas Instruments TI-84 for combinations and permutations. Impressively, a 52 card deck would have 52! arrangements or more than 10 to the 67th power.
Combination vs Permutation
Combinations and Permutations on MathsIsFun
Table of Factorials up to 30
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