Finite Math Examples

${}_{50}C_{5}$

Step 1

Evaluate

${}_{50}C_{5}$ using the formula

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

$\frac{50!}{(50 - 5)! 5!}$

Step 2

Subtract

$5$ from

$50$ .

$\frac{50!}{(45)! 5!}$

Step 3

Simplify

$\frac{50!}{(45)! 5!}$ .

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Step 3.1

Rewrite

$50!$ as

$50 \cdot 49 \cdot 48 \cdot 47 \cdot 46 \cdot 45!$ .

$\frac{50 \cdot 49 \cdot 48 \cdot 47 \cdot 46 \cdot 45!}{(45)! 5!}$

Step 3.2

Cancel the common factor of

$45!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{50 \cdot 49 \cdot 48 \cdot 47 \cdot 46 \cdot 45!}{(45)! 5!}$

Step 3.2.2

Rewrite the expression.

$\frac{50 \cdot 49 \cdot 48 \cdot 47 \cdot 46}{5!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply

$50$ by

$49$ .

$\frac{2450 \cdot 48 \cdot 47 \cdot 46}{5!}$

Step 3.3.2

Multiply

$2450$ by

$48$ .

$\frac{117600 \cdot 47 \cdot 46}{5!}$

Step 3.3.3

Multiply

$117600$ by

$47$ .

$\frac{5527200 \cdot 46}{5!}$

Step 3.3.4

Multiply

$5527200$ by

$46$ .

$\frac{254251200}{5!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$5!$ to

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

$\frac{254251200}{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

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

$4$ .

$\frac{254251200}{20 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2.2

Multiply

$20$ by

$3$ .

$\frac{254251200}{60 \cdot 2 \cdot 1}$

Step 3.4.2.3

Multiply

$60$ by

$2$ .

$\frac{254251200}{120 \cdot 1}$

Step 3.4.2.4

Multiply

$120$ by

$1$ .

$\frac{254251200}{120}$

Step 3.5

Divide

$254251200$ by

$120$ .

$2118760$