Finite Math Examples

7 P 4

${}_{7}P_{4}$

Step 1

Evaluate

7 P 4

${}_{7}P_{4}$ using the formula

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

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

\frac{7!}{(7 - 4)!}

$\frac{7!}{(7 - 4)!}$

Step 2

Subtract

4

$4$ from

7

$7$ .

\frac{7!}{(3)!}

$\frac{7!}{(3)!}$

Step 3

Simplify

\frac{7!}{(3)!}

$\frac{7!}{(3)!}$ .

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Step 3.1

Rewrite

7!

$7!$ as

7 \cdot 6 \cdot 5 \cdot 4 \cdot 3!

$7 \cdot 6 \cdot 5 \cdot 4 \cdot 3!$ .

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

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

Step 3.2

Cancel the common factor of

3!

$3!$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Divide

$7 \cdot 6 \cdot 5 \cdot 4$ by

$1$ .

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

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

Step 3.3

Multiply

$7 \cdot 6 \cdot 5 \cdot 4$ .

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Step 3.3.1

Multiply

$7$ by

$6$ .

$42 \cdot 5 \cdot 4$

Step 3.3.2

Multiply

$42$ by

$5$ .

$210 \cdot 4$

Step 3.3.3

Multiply

$210$ by

$4$ .

$840$

$840$

$840$

${}_{7}P_{4}$

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