Finite Math Examples

${}_{70}C_{5}$

Step 1

Evaluate

${}_{70}C_{5}$ using the formula

${}_{n}C_{r} = \frac{n!}{(n - r)! r!}$ .

$\frac{70!}{(70 - 5)! 5!}$

Step 2

Subtract

$5$ from

$70$ .

$\frac{70!}{(65)! 5!}$

Step 3

Simplify

$\frac{70!}{(65)! 5!}$ .

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Step 3.1

Rewrite

$70!$ as

$70 \cdot 69 \cdot 68 \cdot 67 \cdot 66 \cdot 65!$ .

$\frac{70 \cdot 69 \cdot 68 \cdot 67 \cdot 66 \cdot 65!}{(65)! 5!}$

Step 3.2

Cancel the common factor of

$65!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{70 \cdot 69 \cdot 68 \cdot 67 \cdot 66 \cdot 65!}{(65)! 5!}$

Step 3.2.2

Rewrite the expression.

$\frac{70 \cdot 69 \cdot 68 \cdot 67 \cdot 66}{5!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply

$70$ by

$69$ .

$\frac{4830 \cdot 68 \cdot 67 \cdot 66}{5!}$

Step 3.3.2

Multiply

$4830$ by

$68$ .

$\frac{328440 \cdot 67 \cdot 66}{5!}$

Step 3.3.3

Multiply

$328440$ by

$67$ .

$\frac{22005480 \cdot 66}{5!}$

Step 3.3.4

Multiply

$22005480$ by

$66$ .

$\frac{1452361680}{5!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$5!$ to

$5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{1452361680}{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2

Multiply

$5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 3.4.2.1

Multiply

$5$ by

$4$ .

$\frac{1452361680}{20 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2.2

Multiply

$20$ by

$3$ .

$\frac{1452361680}{60 \cdot 2 \cdot 1}$

Step 3.4.2.3

Multiply

$60$ by

$2$ .

$\frac{1452361680}{120 \cdot 1}$

Step 3.4.2.4

Multiply

$120$ by

$1$ .

$\frac{1452361680}{120}$

Step 3.5

Divide

$1452361680$ by

$120$ .

$12103014$