Precalculus Examples

${}_{1000}C_{999}$

Step 1

Evaluate ${}_{1000}C_{999}$ using the formula ${}_{n}C_{r} = \frac{n!}{(n - r)! r!}$ .

$\frac{1000!}{(1000 - 999)! 999!}$

Step 2

Subtract $999$ from $1000$ .

$\frac{1000!}{(1)! 999!}$

Step 3

Simplify $\frac{1000!}{(1)! 999!}$ .

Tap for more steps...

Step 3.1

Rewrite $1000!$ as $1000 \cdot 999!$ .

$\frac{1000 \cdot 999!}{(1)! 999!}$

Step 3.2

Cancel the common factor of $999!$ .

Tap for more steps...

Step 3.2.1

Cancel the common factor.

$\frac{1000 \cdot 999!}{(1)! 999!}$

Step 3.2.2

Rewrite the expression.

$\frac{1000}{(1)!}$

Step 3.3

Expand $(1)!$ to $1$ .

$\frac{1000}{1}$

Step 3.4

Divide $1000$ by $1$ .

$1000$