Finite Math Examples

6 P 4

${}_{6}P_{4}$

Step 1

Evaluate

6 P 4

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

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

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

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

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

Step 2

Subtract

4

$4$ from

6

$6$ .

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

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

Step 3

Simplify

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

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

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Step 3.1

Rewrite

6!

$6!$ as

6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!

$6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!$ .

\frac{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!}{(2)!}

$\frac{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!}{(2)!}$

Step 3.2

Cancel the common factor of

2!

$2!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!}{(2)!}$

Step 3.2.2

Divide

$6 \cdot 5 \cdot 4 \cdot 3$ by

$1$ .

$6 \cdot 5 \cdot 4 \cdot 3$

$6 \cdot 5 \cdot 4 \cdot 3$

Step 3.3

Multiply

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

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Step 3.3.1

Multiply

$6$ by

$5$ .

$30 \cdot 4 \cdot 3$

Step 3.3.2

Multiply

$30$ by

$4$ .

$120 \cdot 3$

Step 3.3.3

Multiply

$120$ by

$3$ .

$360$

$360$

$360$

${}_{6}P_{4}$

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