Question

21!/13!
Evaluate the factorial expression

Answer 1

8204716800

Explanation:

The expression
`\( (21!)/(13!) \)` involves factorials, and we can simplify it using the properties of factorials.

The factorial of a number n is the product of all positive integers up to n. For example,
`\( 5! = 5 * 4 * 3 * 2 * 1 \)`.

In the expression
`\( (21!)/(13!) \)`:

Cancel out common factors:

`\[ (21!)/(13!) = (21 * 20 * 19 * 18 * 17 * 16 * 15 * 14 * 13!)/(13!) \]`

Cancel out
`\(13!\)`:

`\[ = 21 * 20 * 19 * 18 * 17 * 16 * 15 * 14 \]`

Calculate the result:

`\[ = 8204716800 \]`

So,
`\( (21!)/(13!) = 8204716800 \)`.

The cancellation of the common factors (in this case, \(13!\)) simplifies the expression, and you're left with the product of the remaining numbers. If you have any further questions, feel free to ask!