5.2.1—Permutations and combinations

nPr counts ordered arrangements of r objects from n; nCr counts unordered selections. Use nPr=n!/(n−r)! and nCr=n!/[r!(n−r)!].

Decide whether positions matter before choosing a formula, and avoid counting the same outcome under different descriptions.

Choosing president and secretary from 8 people uses 8P2; choosing a two-person committee uses 8C2.

The same two people can form two ordered roles but only one unordered committee.