Finite Math Examples

${}_{13}C_{3}$

Step 1

Evaluate ${}_{13}C_{3}$ using the formula ${}_{n}C_{r} = \frac{n!}{(n - r)! r!}$ .

$\frac{13!}{(13 - 3)! 3!}$

Step 2

Subtract $3$ from $13$ .

$\frac{13!}{(10)! 3!}$

Step 3

Simplify $\frac{13!}{(10)! 3!}$ .

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Step 3.1

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

$\frac{13 \cdot 12 \cdot 11 \cdot 10!}{(10)! 3!}$

Step 3.2

Cancel the common factor of $10!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{13 \cdot 12 \cdot 11 \cdot 10!}{(10)! 3!}$

Step 3.2.2

Rewrite the expression.

$\frac{13 \cdot 12 \cdot 11}{3!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply $13$ by $12$ .

$\frac{156 \cdot 11}{3!}$

Step 3.3.2

Multiply $156$ by $11$ .

$\frac{1716}{3!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

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

$\frac{1716}{3 \cdot 2 \cdot 1}$

Step 3.4.2

Multiply $3 \cdot 2 \cdot 1$ .

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Step 3.4.2.1

Multiply $3$ by $2$ .

$\frac{1716}{6 \cdot 1}$

Step 3.4.2.2

Multiply $6$ by $1$ .

$\frac{1716}{6}$

Step 3.5

Divide $1716$ by $6$ .

$286$