Finite Math Examples

$2 \cdot \frac{8!}{5!}$

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

Multiply $8$ by $7$ .

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

Step 1.2.2

Multiply $56$ by $6$ .

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

Step 1.2.3

Multiply $336$ by $5$ .

$2 \cdot \frac{1680 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{5!}$

Step 1.2.4

Multiply $1680$ by $4$ .

$2 \cdot \frac{6720 \cdot 3 \cdot 2 \cdot 1}{5!}$

Step 1.2.5

Multiply $6720$ by $3$ .

$2 \cdot \frac{20160 \cdot 2 \cdot 1}{5!}$

Step 1.2.6

Multiply $20160$ by $2$ .

$2 \cdot \frac{40320 \cdot 1}{5!}$

Step 1.2.7

Multiply $40320$ by $1$ .

$2 \cdot \frac{40320}{5!}$

Step 2

Simplify the denominator.

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Step 2.1

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

$2 \cdot \frac{40320}{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Step 2.2

Multiply $5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 2.2.1

Multiply $5$ by $4$ .

$2 \cdot \frac{40320}{20 \cdot 3 \cdot 2 \cdot 1}$

Step 2.2.2

Multiply $20$ by $3$ .

$2 \cdot \frac{40320}{60 \cdot 2 \cdot 1}$

Step 2.2.3

Multiply $60$ by $2$ .

$2 \cdot \frac{40320}{120 \cdot 1}$

Step 2.2.4

Multiply $120$ by $1$ .

$2 \cdot \frac{40320}{120}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Factor $2$ out of $120$ .

$2 \cdot \frac{40320}{2 (60)}$

Step 3.1.2

Cancel the common factor.

$2 \cdot \frac{40320}{2 \cdot 60}$

Step 3.1.3

Rewrite the expression.

$\frac{40320}{60}$

Step 3.2

Divide $40320$ by $60$ .

$672$