Practice Factorial in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Worksheet PDF Free Answer-key PDF Family

Quick Recap

The factorial of a non-negative integer nn, written n!n!, is the product of all positive integers from 1 to nn: n!=n⋅(n−1)⋯2⋅1n! = n \cdot (n-1) \cdots 2 \cdot 1.

Factorial counts the number of ways to arrange nn distinct objects in a row — for 3 items, there are 3!=63! = 6 possible orderings.

Showing a random 20 of 50 problems.

Example 1

medium
Compute 6!2! 2! 2!\frac{6!}{2!\,2!\,2!}.

Example 2

medium
Compute (83)\binom{8}{3} using factorials.

Example 3

easy
Compute 6!6!.

Example 4

easy
Compute 7!7!\frac{7!}{7!}.

Example 5

medium
How many distinct 44-digit codes use digits 1,2,3,41,2,3,4 each exactly once?

Example 6

easy
What is 9!7!\dfrac{9!}{7!}?

Example 7

easy
Why is 0!0! defined as 11?

Example 8

medium
In how many ways can a President, Vice-President, and Secretary be chosen from 1010 club members (no double roles)?

Example 9

medium
Compute 9!3! 6!\frac{9!}{3!\,6!}.

Example 10

easy
Compute 3!+2!3!+2!.

Example 11

easy
In how many ways can 33 distinct friends sit in 33 chairs in a row?

Example 12

hard
Solve for nn in (n2)=45\binom{n}{2}=45.

Example 13

medium
Simplify 10!8!\frac{10!}{8!}.

Example 14

easy
Compute 5!3!2!\dfrac{5!}{3!2!}.

Example 15

medium
How many trailing zeros does 10!10! have?

Example 16

medium
Simplify (n+1)!n!\frac{(n+1)!}{n!}.

Example 17

hard
Compute the largest power of 22 that divides 10!10!.

Example 18

easy
Compute 1!1!.

Example 19

challenge
Find the number of trailing zeros in 100!100!.

Example 20

hard
How many distinct arrangements of the letters in 'MATHEMATICS' (11 letters) exist?
← Back to Factorial Worked Examples Formula Explained