Finite Math Examples

10 P 3

${}_{10}P_{3}$

Step 1

Evaluate

10 P 3

${}_{10}P_{3}$ using the formula

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

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

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

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

Step 2

Subtract

3

$3$ from

10

$10$ .

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

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

Step 3

Simplify

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

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

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Step 3.1

Rewrite

10!

$10!$ as

10 \cdot 9 \cdot 8 \cdot 7!

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

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

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

Step 3.2

Cancel the common factor of

7!

$7!$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Divide

$10 \cdot 9 \cdot 8$ by

$1$ .

$10 \cdot 9 \cdot 8$

$10 \cdot 9 \cdot 8$

Step 3.3

Multiply

$10 \cdot 9 \cdot 8$ .

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Step 3.3.1

Multiply

$10$ by

$9$ .

$90 \cdot 8$

Step 3.3.2

Multiply

$90$ by

$8$ .

$720$

$720$

$720$

${}_{10}P_{3}$

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$