Finite Math Examples

${}_{11}C_{5}$

Step 1

Evaluate

${}_{11}C_{5}$ using the formula

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

$\frac{11!}{(11 - 5)! 5!}$

Step 2

Subtract

$5$ from

$11$ .

$\frac{11!}{(6)! 5!}$

Step 3

Simplify

$\frac{11!}{(6)! 5!}$ .

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Step 3.1

Rewrite

$11!$ as

$11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6!$ .

$\frac{11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6!}{(6)! 5!}$

Step 3.2

Cancel the common factor of

$6!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6!}{(6)! 5!}$

Step 3.2.2

Rewrite the expression.

$\frac{11 \cdot 10 \cdot 9 \cdot 8 \cdot 7}{5!}$

$\frac{11 \cdot 10 \cdot 9 \cdot 8 \cdot 7}{5!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply

$11$ by

$10$ .

$\frac{110 \cdot 9 \cdot 8 \cdot 7}{5!}$

Step 3.3.2

Multiply

$110$ by

$9$ .

$\frac{990 \cdot 8 \cdot 7}{5!}$

Step 3.3.3

Multiply

$990$ by

$8$ .

$\frac{7920 \cdot 7}{5!}$

Step 3.3.4

Multiply

$7920$ by

$7$ .

$\frac{55440}{5!}$

$\frac{55440}{5!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$5!$ to

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

$\frac{55440}{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

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

$4$ .

$\frac{55440}{20 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2.2

Multiply

$20$ by

$3$ .

$\frac{55440}{60 \cdot 2 \cdot 1}$

Step 3.4.2.3

Multiply

$60$ by

$2$ .

$\frac{55440}{120 \cdot 1}$

Step 3.4.2.4

Multiply

$120$ by

$1$ .

$\frac{55440}{120}$

$\frac{55440}{120}$

$\frac{55440}{120}$

Step 3.5

Divide

$55440$ by

$120$ .

$462$

$462$

${}_{11}C_{5}$

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$