Finite Math Examples

${}_{30}C_{3}$

Step 1

Evaluate ${}_{30}C_{3}$ using the formula ${}_{n}C_{r} = \frac{n!}{(n - r)! r!}$ .

$\frac{30!}{(30 - 3)! 3!}$

Step 2

Subtract $3$ from $30$ .

$\frac{30!}{(27)! 3!}$

Step 3

Simplify $\frac{30!}{(27)! 3!}$ .

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Step 3.1

Rewrite $30!$ as $30 \cdot 29 \cdot 28 \cdot 27!$ .

$\frac{30 \cdot 29 \cdot 28 \cdot 27!}{(27)! 3!}$

Step 3.2

Cancel the common factor of $27!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{30 \cdot 29 \cdot 28 \cdot 27!}{(27)! 3!}$

Step 3.2.2

Rewrite the expression.

$\frac{30 \cdot 29 \cdot 28}{3!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply $30$ by $29$ .

$\frac{870 \cdot 28}{3!}$

Step 3.3.2

Multiply $870$ by $28$ .

$\frac{24360}{3!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

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

$\frac{24360}{3 \cdot 2 \cdot 1}$

Step 3.4.2

Multiply $3 \cdot 2 \cdot 1$ .

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Step 3.4.2.1

Multiply $3$ by $2$ .

$\frac{24360}{6 \cdot 1}$

Step 3.4.2.2

Multiply $6$ by $1$ .

$\frac{24360}{6}$

Step 3.5

Divide $24360$ by $6$ .

$4060$