Finite Math Examples

${}_{14}C_{5}$

Step 1

Evaluate ${}_{14}C_{5}$ using the formula ${}_{n}C_{r} = \frac{n!}{(n - r)! r!}$ .

$\frac{14!}{(14 - 5)! 5!}$

Step 2

Subtract $5$ from $14$ .

$\frac{14!}{(9)! 5!}$

Step 3

Simplify $\frac{14!}{(9)! 5!}$ .

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Step 3.1

Rewrite $14!$ as $14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9!$ .

$\frac{14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9!}{(9)! 5!}$

Step 3.2

Cancel the common factor of $9!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9!}{(9)! 5!}$

Step 3.2.2

Rewrite the expression.

$\frac{14 \cdot 13 \cdot 12 \cdot 11 \cdot 10}{5!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply $14$ by $13$ .

$\frac{182 \cdot 12 \cdot 11 \cdot 10}{5!}$

Step 3.3.2

Multiply $182$ by $12$ .

$\frac{2184 \cdot 11 \cdot 10}{5!}$

Step 3.3.3

Multiply $2184$ by $11$ .

$\frac{24024 \cdot 10}{5!}$

Step 3.3.4

Multiply $24024$ by $10$ .

$\frac{240240}{5!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand $5!$ to $5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{240240}{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

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 $4$ .

$\frac{240240}{20 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2.2

Multiply $20$ by $3$ .

$\frac{240240}{60 \cdot 2 \cdot 1}$

Step 3.4.2.3

Multiply $60$ by $2$ .

$\frac{240240}{120 \cdot 1}$

Step 3.4.2.4

Multiply $120$ by $1$ .

$\frac{240240}{120}$

Step 3.5

Divide $240240$ by $120$ .

$2002$