Finite Math Examples

${}_{7}P_{5}$

Step 1

Evaluate

${}_{7}P_{5}$ using the formula

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

$\frac{7!}{(7 - 5)!}$

Step 2

Subtract

$5$ from

$7$ .

$\frac{7!}{(2)!}$

Step 3

Simplify

$\frac{7!}{(2)!}$ .

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Step 3.1

Rewrite

$7!$ as

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

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

Step 3.2

Cancel the common factor of

$2!$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Divide

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

$1$ .

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

Step 3.3

Multiply

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

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Step 3.3.1

Multiply

$7$ by

$6$ .

$42 \cdot 5 \cdot 4 \cdot 3$

Step 3.3.2

Multiply

$42$ by

$5$ .

$210 \cdot 4 \cdot 3$

Step 3.3.3

Multiply

$210$ by

$4$ .

$840 \cdot 3$

Step 3.3.4

Multiply

$840$ by

$3$ .

$2520$

${}_{7}P_{5}$

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