Arrangements (Permutations) (Leaving Cert Mathematics): Flashcards

Different ways to order/sequence distinct objects

6 (ABC, ACB, BAC, BCA, CAB, CBA)

$n \times (n-1) \times (n-2) \times ... \times 2 \times 1$

$3 \times 2 \times 1 = 6$

$5 \times 4 \times 3 \times 2 \times 1 = 120$

$n!$

Count choices for each position, multiply together

Fill restriction boxes first, then remaining positions

Treat as one unit, multiply by internal arrangements

$7! = 5040$

Order matters