Finite Math Examples

${}_{26}C_{5}$

Step 1

Evaluate ${}_{26}C_{5}$ using the formula ${}_{n}C_{r} = \frac{n!}{(n - r)! r!}$ .

$\frac{26!}{(26 - 5)! 5!}$

Step 2

Subtract $5$ from $26$ .

$\frac{26!}{(21)! 5!}$

Step 3

Simplify $\frac{26!}{(21)! 5!}$ .

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Step 3.1

Rewrite $26!$ as $26 \cdot 25 \cdot 24 \cdot 23 \cdot 22 \cdot 21!$ .

$\frac{26 \cdot 25 \cdot 24 \cdot 23 \cdot 22 \cdot 21!}{(21)! 5!}$

Step 3.2

Cancel the common factor of $21!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{26 \cdot 25 \cdot 24 \cdot 23 \cdot 22 \cdot 21!}{(21)! 5!}$

Step 3.2.2

Rewrite the expression.

$\frac{26 \cdot 25 \cdot 24 \cdot 23 \cdot 22}{5!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply $26$ by $25$ .

$\frac{650 \cdot 24 \cdot 23 \cdot 22}{5!}$

Step 3.3.2

Multiply $650$ by $24$ .

$\frac{15600 \cdot 23 \cdot 22}{5!}$

Step 3.3.3

Multiply $15600$ by $23$ .

$\frac{358800 \cdot 22}{5!}$

Step 3.3.4

Multiply $358800$ by $22$ .

$\frac{7893600}{5!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

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

$\frac{7893600}{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

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 $4$ .

$\frac{7893600}{20 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2.2

Multiply $20$ by $3$ .

$\frac{7893600}{60 \cdot 2 \cdot 1}$

Step 3.4.2.3

Multiply $60$ by $2$ .

$\frac{7893600}{120 \cdot 1}$

Step 3.4.2.4

Multiply $120$ by $1$ .

$\frac{7893600}{120}$

Step 3.5

Divide $7893600$ by $120$ .

$65780$