Finite Math Examples

10 P 7

${}_{10}P_{7}$

Step 1

Evaluate

10 P 7

${}_{10}P_{7}$ using the formula

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

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

\frac{10!}{(10 - 7)!}

$\frac{10!}{(10 - 7)!}$

Step 2

Subtract

7

$7$ from

10

$10$ .

\frac{10!}{(3)!}

$\frac{10!}{(3)!}$

Step 3

Simplify

\frac{10!}{(3)!}

$\frac{10!}{(3)!}$ .

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Step 3.1

Rewrite

10!

$10!$ as

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

$10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3!$ .

\frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3!}{(3)!}

$\frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3!}{(3)!}$

Step 3.2

Cancel the common factor of

3!

$3!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3!}{(3)!}$

Step 3.2.2

Divide

$10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4$ by

$1$ .

$10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4$

Step 3.3

Multiply

$10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4$ .

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Step 3.3.1

Multiply

$10$ by

$9$ .

$90 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4$

Step 3.3.2

Multiply

$90$ by

$8$ .

$720 \cdot 7 \cdot 6 \cdot 5 \cdot 4$

Step 3.3.3

Multiply

$720$ by

$7$ .

$5040 \cdot 6 \cdot 5 \cdot 4$

Step 3.3.4

Multiply

$5040$ by

$6$ .

$30240 \cdot 5 \cdot 4$

Step 3.3.5

Multiply

$30240$ by

$5$ .

$151200 \cdot 4$

Step 3.3.6

Multiply

$151200$ by

$4$ .

$604800$

${}_{10}P_{7}$

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