Finite Math Examples

6 C 3

${}_{6}C_{3}$

Step 1

Evaluate

6 C 3

${}_{6}C_{3}$ using the formula

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

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

\frac{6!}{(6 - 3)! 3!}

$\frac{6!}{(6 - 3)! 3!}$

Step 2

Subtract

3

$3$ from

6

$6$ .

\frac{6!}{(3)! 3!}

$\frac{6!}{(3)! 3!}$

Step 3

Simplify

\frac{6!}{(3)! 3!}

$\frac{6!}{(3)! 3!}$ .

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Step 3.1

Rewrite

6!

$6!$ as

6 \cdot 5 \cdot 4 \cdot 3!

$6 \cdot 5 \cdot 4 \cdot 3!$ .

\frac{6 \cdot 5 \cdot 4 \cdot 3!}{(3)! 3!}

$\frac{6 \cdot 5 \cdot 4 \cdot 3!}{(3)! 3!}$

Step 3.2

Cancel the common factor of

3!

$3!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{6 \cdot 5 \cdot 4 \cdot 3!}{(3)! 3!}$

Step 3.2.2

Rewrite the expression.

$\frac{6 \cdot 5 \cdot 4}{3!}$

$\frac{6 \cdot 5 \cdot 4}{3!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply

$6$ by

$5$ .

$\frac{30 \cdot 4}{3!}$

Step 3.3.2

Multiply

$30$ by

$4$ .

$\frac{120}{3!}$

$\frac{120}{3!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$3!$ to

$3 \cdot 2 \cdot 1$ .

$\frac{120}{3 \cdot 2 \cdot 1}$

Step 3.4.2

Multiply

$3 \cdot 2 \cdot 1$ .

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Step 3.4.2.1

Multiply

$3$ by

$2$ .

$\frac{120}{6 \cdot 1}$

Step 3.4.2.2

Multiply

$6$ by

$1$ .

$\frac{120}{6}$

$\frac{120}{6}$

$\frac{120}{6}$

Step 3.5

Divide

$120$ by

$6$ .

$20$

$20$

${}_{6}C_{3}$

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