Permutations count ordered lists: nPr = n! / (n − r)!. Order matters. President, treasurer, secretary from 10 people is P(10, 3) = 720. Unordered groups are combinations, in permutations versus combinations.
Arrange, do not just choose
If swapping two people makes a new outcome, use nPr. The combinations formula is nCr, in the combinations formula. The counting principle is the product of choices, in the counting principle.
The short list is in ACT Math formulas.
The bottom line
Ordered slots: nPr. Drop the r! in the denominator that combinations use.
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