Finite Math Examples

10 P 5

${}_{10}P_{5}$

Step 1

Evaluate

10 P 5

${}_{10}P_{5}$ using the formula

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

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

\frac{10!}{(10 - 5)!}

$\frac{10!}{(10 - 5)!}$

Step 2

Subtract

5

$5$ from

10

$10$ .

\frac{10!}{(5)!}

$\frac{10!}{(5)!}$

Step 3

Simplify

\frac{10!}{(5)!}

$\frac{10!}{(5)!}$ .

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Step 3.1

Rewrite

10!

$10!$ as

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

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

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

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

Step 3.2

Cancel the common factor of

5!

$5!$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Divide

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

$1$ .

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

Step 3.3

Multiply

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

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Step 3.3.1

Multiply

$10$ by

$9$ .

$90 \cdot 8 \cdot 7 \cdot 6$

Step 3.3.2

Multiply

$90$ by

$8$ .

$720 \cdot 7 \cdot 6$

Step 3.3.3

Multiply

$720$ by

$7$ .

$5040 \cdot 6$

Step 3.3.4

Multiply

$5040$ by

$6$ .

$30240$

${}_{10}P_{5}$

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