Finite Math Examples

{}_{6}C_{4}

${}_{6}C_{4}$

Step 1

Evaluate

{}_{6}C_{4}

${}_{6}C_{4}$ using the formula

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

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

\frac{6!}{(6 - 4)! 4!}

$\frac{6!}{(6 - 4)! 4!}$

Step 2

Subtract

4

$4$ from

6

$6$ .

\frac{6!}{(2)! 4!}

$\frac{6!}{(2)! 4!}$

Step 3

Simplify

\frac{6!}{(2)! 4!}

$\frac{6!}{(2)! 4!}$ .

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Step 3.1

Rewrite

6!

$6!$ as

6 \cdot 5 \cdot 4!

$6 \cdot 5 \cdot 4!$ .

\frac{6 \cdot 5 \cdot 4!}{(2)! 4!}

$\frac{6 \cdot 5 \cdot 4!}{(2)! 4!}$

Step 3.2

Cancel the common factor of

4!

$4!$ .

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Step 3.2.1

Cancel the common factor.

\frac{6 \cdot 5 \cdot 4!}{(2)! 4!}

$\frac{6 \cdot 5 \cdot 4!}{(2)! 4!}$

Step 3.2.2

Rewrite the expression.

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

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

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

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

Step 3.3

Multiply

6

$6$ by

5

$5$ .

\frac{30}{(2)!}

$\frac{30}{(2)!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

(2)!

$(2)!$ to

2 \cdot 1

$2 \cdot 1$ .

\frac{30}{2 \cdot 1}

$\frac{30}{2 \cdot 1}$

Step 3.4.2

Multiply

2

$2$ by

1

$1$ .

\frac{30}{2}

$\frac{30}{2}$

\frac{30}{2}

$\frac{30}{2}$

Step 3.5

Divide

30

$30$ by

2

$2$ .

15

$15$

15

$15$

{}_{6}C_{4}

${}_{6}C_{4}$

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

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