Basic Math Examples

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

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

Step 1

Rewrite

10!

$10!$ as

10 \cdot 9 \cdot 8 \cdot 7 \cdot 6!

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

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

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

Step 2

Cancel the common factor of

6!

$6!$ .

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Step 2.1

Cancel the common factor.

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

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

Step 2.2

Rewrite the expression.

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

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

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

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

Step 3

Simplify the numerator.

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Step 3.1

Multiply

10

$10$ by

9

$9$ .

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

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

Step 3.2

Multiply

90

$90$ by

8

$8$ .

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

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

Step 3.3

Multiply

720

$720$ by

7

$7$ .

\frac{5040}{4!}

$\frac{5040}{4!}$

\frac{5040}{4!}

$\frac{5040}{4!}$

Step 4

Simplify the denominator.

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Step 4.1

Expand

4!

$4!$ to

4 \cdot 3 \cdot 2 \cdot 1

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

\frac{5040}{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

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

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Step 4.2.1

Multiply

4

$4$ by

3

$3$ .

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

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

Step 4.2.2

Multiply

12

$12$ by

2

$2$ .

\frac{5040}{24 \cdot 1}

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

Step 4.2.3

Multiply

24

$24$ by

1

$1$ .

\frac{5040}{24}

$\frac{5040}{24}$

\frac{5040}{24}

$\frac{5040}{24}$

\frac{5040}{24}

$\frac{5040}{24}$

Step 5

Divide

5040

$5040$ by

24

$24$ .

210

$210$

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

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

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