Finite Math Examples

${}_{8}C_{7}$

Step 1

Evaluate ${}_{8}C_{7}$ using the formula ${}_{n}C_{r} = \frac{n!}{(n - r)! r!}$ .

$\frac{8!}{(8 - 7)! 7!}$

Step 2

Subtract $7$ from $8$ .

$\frac{8!}{(1)! 7!}$

Step 3

Simplify $\frac{8!}{(1)! 7!}$ .

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Step 3.1

Rewrite $8!$ as $8 \cdot 7!$ .

$\frac{8 \cdot 7!}{(1)! 7!}$

Step 3.2

Cancel the common factor of $7!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{8 \cdot 7!}{(1)! 7!}$

Step 3.2.2

Rewrite the expression.

$\frac{8}{(1)!}$

Step 3.3

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

$\frac{8}{1}$

Step 3.4

Divide $8$ by $1$ .

$8$