Finite Math Examples

$\frac{12!}{(6!) (6!)}$

Step 1

Rewrite $12!$ as $12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6!$ .

$\frac{12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6!}{6! 6!}$

Step 2

Cancel the common factor of $6!$ .

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Step 2.1

Cancel the common factor.

$\frac{12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6!}{6! 6!}$

Step 2.2

Rewrite the expression.

$\frac{12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7}{6!}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $12$ by $11$ .

$\frac{132 \cdot 10 \cdot 9 \cdot 8 \cdot 7}{6!}$

Step 3.2

Multiply $132$ by $10$ .

$\frac{1320 \cdot 9 \cdot 8 \cdot 7}{6!}$

Step 3.3

Multiply $1320$ by $9$ .

$\frac{11880 \cdot 8 \cdot 7}{6!}$

Step 3.4

Multiply $11880$ by $8$ .

$\frac{95040 \cdot 7}{6!}$

Step 3.5

Multiply $95040$ by $7$ .

$\frac{665280}{6!}$

Step 4

Simplify the denominator.

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Step 4.1

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

$\frac{665280}{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Step 4.2

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

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Step 4.2.1

Multiply $6$ by $5$ .

$\frac{665280}{30 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Step 4.2.2

Multiply $30$ by $4$ .

$\frac{665280}{120 \cdot 3 \cdot 2 \cdot 1}$

Step 4.2.3

Multiply $120$ by $3$ .

$\frac{665280}{360 \cdot 2 \cdot 1}$

Step 4.2.4

Multiply $360$ by $2$ .

$\frac{665280}{720 \cdot 1}$

Step 4.2.5

Multiply $720$ by $1$ .

$\frac{665280}{720}$

Step 5

Divide $665280$ by $720$ .

$924$