Finite Math Examples

${}_{8}P_{5}$

Step 1

Evaluate

${}_{8}P_{5}$ using the formula

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

$\frac{8!}{(8 - 5)!}$

Step 2

Subtract

$5$ from

$8$ .

$\frac{8!}{(3)!}$

Step 3

Simplify

$\frac{8!}{(3)!}$ .

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Step 3.1

Rewrite

$8!$ as

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

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

Step 3.2

Cancel the common factor of

$3!$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Divide

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

$1$ .

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

Step 3.3

Multiply

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

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Step 3.3.1

Multiply

$8$ by

$7$ .

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

Step 3.3.2

Multiply

$56$ by

$6$ .

$336 \cdot 5 \cdot 4$

Step 3.3.3

Multiply

$336$ by

$5$ .

$1680 \cdot 4$

Step 3.3.4

Multiply

$1680$ by

$4$ .

$6720$

${}_{8}P_{5}$

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