Unformatted text preview: o the sum rule: a basic counting technique, which states that the number of ways to do a task in one of two ways is the sum of the number of ways to do these tasks if they cannot be done simultaneously o the pigeonhole principle: When more than k objects are placed in k boxes, there must be a box containing more than one object o the generalized pigeonhole principle: When N objects are placed in k boxes, there must be a box containing at least k N / objects o ( 29 ( 29 ! ! , r n n r n P-= o ( 29 ( 29 ! ! ! , r n r n r n r n C-= = o Pascal’s Identity: + -= + k n k n k n 1 1 o the Binomial Theorem: ( 29 ∑ =- = + n k k k n n y x k n y x...
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- Fall '07
- Combinatorics, Generalized Pigeonhole Principle, basic counting technique