Finite Math Examples

7 C 5

${}_{7}C_{5}$

Step 1

Evaluate

7 C 5

${}_{7}C_{5}$ using the formula

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

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

\frac{7!}{(7 - 5)! 5!}

$\frac{7!}{(7 - 5)! 5!}$

Step 2

Subtract

5

$5$ from

7

$7$ .

\frac{7!}{(2)! 5!}

$\frac{7!}{(2)! 5!}$

Step 3

Simplify

\frac{7!}{(2)! 5!}

$\frac{7!}{(2)! 5!}$ .

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Step 3.1

Rewrite

7!

$7!$ as

7 \cdot 6 \cdot 5!

$7 \cdot 6 \cdot 5!$ .

\frac{7 \cdot 6 \cdot 5!}{(2)! 5!}

$\frac{7 \cdot 6 \cdot 5!}{(2)! 5!}$

Step 3.2

Cancel the common factor of

5!

$5!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{7 \cdot 6 \cdot 5!}{(2)! 5!}$

Step 3.2.2

Rewrite the expression.

$\frac{7 \cdot 6}{(2)!}$

$\frac{7 \cdot 6}{(2)!}$

Step 3.3

Multiply

$7$ by

$6$ .

$\frac{42}{(2)!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$(2)!$ to

$2 \cdot 1$ .

$\frac{42}{2 \cdot 1}$

Step 3.4.2

Multiply

$2$ by

$1$ .

$\frac{42}{2}$

$\frac{42}{2}$

Step 3.5

Divide

$42$ by

$2$ .

$21$

$21$

${}_{7}C_{5}$

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