Arrangements and Factorials Worksheet with Answer Key

What's on the worksheet

1. Simplify the factorial expressions without working out any factorial in full.
   \dfrac{5! \times 6!}{4! \times 7!}\dfrac{(n - 1)!}{(n + 1)!}\dfrac{(n + 1)!}{(n + 1)\,(n - 1)!}\dfrac{(2n)!}{(2n - 2)!}\dfrac{n! \times n!}{(n + 1)! \times (n - 1)!}
2. Count arrangements of PLUMBING and check Maya's claim about LETTER.
3. Find the whole number n for a factorial equation and explain why there is one answer.
4. Find when n factorial first exceeds 3 to the n and compare the sequence.
5. Word problem: arranging 8 macarons in a ring on a turning plate.
6. Word problem: arranging six beads on a bracelet that can be turned and flipped.