Finite Math Examples

$\frac{10!}{2! (10 - 2)}$

Step 1

Rewrite $10!$ as $10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!$ .

$\frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!}{2! (10 - 2)}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $10$ and $10 - 2$ .

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Step 2.1.1

Factor $2$ out of $10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!$ .

$\frac{2 (5 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!)}{2! (10 - 2)}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $2$ out of $2! (10 - 2)$ .

$\frac{2 (5 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!)}{2 (2! (5 - 1))}$

Step 2.1.2.2

Cancel the common factor.

$\frac{2 (5 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!)}{2 (2! (5 - 1))}$

Step 2.1.2.3

Rewrite the expression.

$\frac{5 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!}{2! (5 - 1)}$

Step 2.2

Cancel the common factor of $2!$ .

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Step 2.2.1

Cancel the common factor.

$\frac{5 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!}{2! (5 - 1)}$

Step 2.2.2

Rewrite the expression.

$\frac{5 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3}{5 - 1}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $5$ by $9$ .

$\frac{45 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3}{5 - 1}$

Step 3.2

Multiply $45$ by $8$ .

$\frac{360 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3}{5 - 1}$

Step 3.3

Multiply $360$ by $7$ .

$\frac{2520 \cdot 6 \cdot 5 \cdot 4 \cdot 3}{5 - 1}$

Step 3.4

Multiply $2520$ by $6$ .

$\frac{15120 \cdot 5 \cdot 4 \cdot 3}{5 - 1}$

Step 3.5

Multiply $15120$ by $5$ .

$\frac{75600 \cdot 4 \cdot 3}{5 - 1}$

Step 3.6

Multiply $75600$ by $4$ .

$\frac{302400 \cdot 3}{5 - 1}$

Step 3.7

Multiply $302400$ by $3$ .

$\frac{907200}{5 - 1}$

Step 4

Simplify the expression.

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Step 4.1

Subtract $1$ from $5$ .

$\frac{907200}{4}$

Step 4.2

Divide $907200$ by $4$ .

$226800$