Basic Math Examples

$\frac{10!}{4! 6!}$

Step 1

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

$\frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6!}{4! 6!}$

Step 2

Cancel the common factor of $6!$ .

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Step 2.1

Cancel the common factor.

$\frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6!}{4! 6!}$

Step 2.2

Rewrite the expression.

$\frac{10 \cdot 9 \cdot 8 \cdot 7}{4!}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $10$ by $9$ .

$\frac{90 \cdot 8 \cdot 7}{4!}$

Step 3.2

Multiply $90$ by $8$ .

$\frac{720 \cdot 7}{4!}$

Step 3.3

Multiply $720$ by $7$ .

$\frac{5040}{4!}$

Step 4

Simplify the denominator.

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Step 4.1

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

$\frac{5040}{4 \cdot 3 \cdot 2 \cdot 1}$

Step 4.2

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

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Step 4.2.1

Multiply $4$ by $3$ .

$\frac{5040}{12 \cdot 2 \cdot 1}$

Step 4.2.2

Multiply $12$ by $2$ .

$\frac{5040}{24 \cdot 1}$

Step 4.2.3

Multiply $24$ by $1$ .

$\frac{5040}{24}$

Step 5

Divide $5040$ by $24$ .

$210$