Finite Math Examples

11 C 4

${}_{11}C_{4}$

Step 1

Evaluate

11 C 4

${}_{11}C_{4}$ using the formula

n C r = \frac{n!}{(n - r)! r!}

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

\frac{11!}{(11 - 4)! 4!}

$\frac{11!}{(11 - 4)! 4!}$

Step 2

Subtract

4

$4$ from

11

$11$ .

\frac{11!}{(7)! 4!}

$\frac{11!}{(7)! 4!}$

Step 3

Simplify

\frac{11!}{(7)! 4!}

$\frac{11!}{(7)! 4!}$ .

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Step 3.1

Rewrite

11!

$11!$ as

11 \cdot 10 \cdot 9 \cdot 8 \cdot 7!

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

\frac{11 \cdot 10 \cdot 9 \cdot 8 \cdot 7!}{(7)! 4!}

$\frac{11 \cdot 10 \cdot 9 \cdot 8 \cdot 7!}{(7)! 4!}$

Step 3.2

Cancel the common factor of

7!

$7!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{11 \cdot 10 \cdot 9 \cdot 8 \cdot 7!}{(7)! 4!}$

Step 3.2.2

Rewrite the expression.

$\frac{11 \cdot 10 \cdot 9 \cdot 8}{4!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply

$11$ by

$10$ .

$\frac{110 \cdot 9 \cdot 8}{4!}$

Step 3.3.2

Multiply

$110$ by

$9$ .

$\frac{990 \cdot 8}{4!}$

Step 3.3.3

Multiply

$990$ by

$8$ .

$\frac{7920}{4!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$4!$ to

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

$\frac{7920}{4 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2

Multiply

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

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Step 3.4.2.1

Multiply

$4$ by

$3$ .

$\frac{7920}{12 \cdot 2 \cdot 1}$

Step 3.4.2.2

Multiply

$12$ by

$2$ .

$\frac{7920}{24 \cdot 1}$

Step 3.4.2.3

Multiply

$24$ by

$1$ .

$\frac{7920}{24}$

Step 3.5

Divide

$7920$ by

$24$ .

$330$

${}_{11}C_{4}$

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