Finite Math Examples

${}_{8}P_{7}$

Step 1

Evaluate ${}_{8}P_{7}$ using the formula ${}_{n}P_{r} = \frac{n!}{(n - r)!}$ .

$\frac{8!}{(8 - 7)!}$

Step 2

Subtract $7$ from $8$ .

$\frac{8!}{(1)!}$

Step 3

Simplify $\frac{8!}{(1)!}$ .

Tap for more steps...

Step 3.1

Simplify the numerator.

Tap for more steps...

Step 3.1.1

Expand $8!$ to $8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2

Multiply $8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

Tap for more steps...

Step 3.1.2.1

Multiply $8$ by $7$ .

$\frac{56 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2.2

Multiply $56$ by $6$ .

$\frac{336 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2.3

Multiply $336$ by $5$ .

$\frac{1680 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2.4

Multiply $1680$ by $4$ .

$\frac{6720 \cdot 3 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2.5

Multiply $6720$ by $3$ .

$\frac{20160 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2.6

Multiply $20160$ by $2$ .

$\frac{40320 \cdot 1}{(1)!}$

Step 3.1.2.7

Multiply $40320$ by $1$ .

$\frac{40320}{(1)!}$

Step 3.2

Expand $(1)!$ to $1$ .

$\frac{40320}{1}$

Step 3.3

Divide $40320$ by $1$ .

$40320$