Finite Math Examples

9 P 7

${}_{9}P_{7}$

Step 1

Evaluate

9 P 7

${}_{9}P_{7}$ using the formula

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

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

\frac{9!}{(9 - 7)!}

$\frac{9!}{(9 - 7)!}$

Step 2

Subtract

7

$7$ from

9

$9$ .

\frac{9!}{(2)!}

$\frac{9!}{(2)!}$

Step 3

Simplify

\frac{9!}{(2)!}

$\frac{9!}{(2)!}$ .

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Step 3.1

Rewrite

9!

$9!$ as

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

$9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!$ .

\frac{9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!}{(2)!}

$\frac{9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!}{(2)!}$

Step 3.2

Cancel the common factor of

2!

$2!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!}{(2)!}$

Step 3.2.2

Divide

$9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3$ by

$1$ .

$9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3$

Step 3.3

Multiply

$9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3$ .

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Step 3.3.1

Multiply

$9$ by

$8$ .

$72 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3$

Step 3.3.2

Multiply

$72$ by

$7$ .

$504 \cdot 6 \cdot 5 \cdot 4 \cdot 3$

Step 3.3.3

Multiply

$504$ by

$6$ .

$3024 \cdot 5 \cdot 4 \cdot 3$

Step 3.3.4

Multiply

$3024$ by

$5$ .

$15120 \cdot 4 \cdot 3$

Step 3.3.5

Multiply

$15120$ by

$4$ .

$60480 \cdot 3$

Step 3.3.6

Multiply

$60480$ by

$3$ .

$181440$

${}_{9}P_{7}$

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