Finite Math Examples

8 P 6

${}_{8}P_{6}$

Step 1

Evaluate

8 P 6

${}_{8}P_{6}$ using the formula

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

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

\frac{8!}{(8 - 6)!}

$\frac{8!}{(8 - 6)!}$

Step 2

Subtract

6

$6$ from

8

$8$ .

\frac{8!}{(2)!}

$\frac{8!}{(2)!}$

Step 3

Simplify

\frac{8!}{(2)!}

$\frac{8!}{(2)!}$ .

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Step 3.1

Rewrite

8!

$8!$ as

8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!

$8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!$ .

\frac{8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!}{(2)!}

$\frac{8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!}{(2)!}$

Step 3.2

Cancel the common factor of

2!

$2!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!}{(2)!}$

Step 3.2.2

Divide

$8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3$ by

$1$ .

$8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3$

Step 3.3

Multiply

$8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3$ .

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Step 3.3.1

Multiply

$8$ by

$7$ .

$56 \cdot 6 \cdot 5 \cdot 4 \cdot 3$

Step 3.3.2

Multiply

$56$ by

$6$ .

$336 \cdot 5 \cdot 4 \cdot 3$

Step 3.3.3

Multiply

$336$ by

$5$ .

$1680 \cdot 4 \cdot 3$

Step 3.3.4

Multiply

$1680$ by

$4$ .

$6720 \cdot 3$

Step 3.3.5

Multiply

$6720$ by

$3$ .

$20160$

${}_{8}P_{6}$

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