Factorial Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

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

Solution

  1. 1
    Rewrite the numerator by expanding 10!10! until it contains 8!8!: 10!=10×9×8!10! = 10 \times 9 \times 8!
  2. 2
    Substitute into the expression: 10!8!=10×9×8!8!\frac{10!}{8!} = \frac{10 \times 9 \times 8!}{8!}
  3. 3
    Cancel 8!8! from numerator and denominator: =10×9=90= 10 \times 9 = 90

Answer

10!8!=90\frac{10!}{8!} = 90
Factorial expressions often simplify by cancellation. Recognizing that n!=n×(n−1)!n! = n \times (n-1)! avoids computing large numbers directly.

About Factorial

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.

Learn more about Factorial →

More Factorial Examples

Example 1 easy

Compute [formula].

Example 3 easy

Evaluate [formula].

Example 4 medium

Solve for [formula]: [formula].

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