Essential Ideas for Section 10.4

Combinations

A combination of r elements selected from a set of n elements is an subset of r elements selected without repetions. The order of selection is not important.

Counting Formulas

Combination formula: The number of ways of selecting r elements from a set with cardinality n in which the order of selection is not important is n!/r!(n - r)!.

Combinations by Pascal's Triangle
The number of ways of selecting r elements from a set with cardinality n in which the order of selection is not important is found by looking at the rth entry in the n row: