Finite Math Examples

${}_{14}P_{7}$

Step 1

Evaluate

${}_{14}P_{7}$ using the formula

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

$\frac{14!}{(14 - 7)!}$

Step 2

Subtract

$7$ from

$14$ .

$\frac{14!}{(7)!}$

Step 3

Simplify

$\frac{14!}{(7)!}$ .

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Step 3.1

Rewrite

$14!$ as

$14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7!$ .

$\frac{14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7!}{(7)!}$

Step 3.2

Cancel the common factor of

$7!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7!}{(7)!}$

Step 3.2.2

Divide

$14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8$ by

$1$ .

$14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8$

Step 3.3

Multiply

$14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8$ .

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Step 3.3.1

Multiply

$14$ by

$13$ .

$182 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8$

Step 3.3.2

Multiply

$182$ by

$12$ .

$2184 \cdot 11 \cdot 10 \cdot 9 \cdot 8$

Step 3.3.3

Multiply

$2184$ by

$11$ .

$24024 \cdot 10 \cdot 9 \cdot 8$

Step 3.3.4

Multiply

$24024$ by

$10$ .

$240240 \cdot 9 \cdot 8$

Step 3.3.5

Multiply

$240240$ by

$9$ .

$2162160 \cdot 8$

Step 3.3.6

Multiply

$2162160$ by

$8$ .

$17297280$