Algebra Examples

$\frac{11!}{4! 4! 2!}$

Step 1

Rewrite $11!$ as $11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4!$ .

$\frac{11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4!}{4! 4! 2!}$

Step 2

Cancel the common factor of $4!$ .

Tap for more steps...

Step 2.1

Cancel the common factor.

$\frac{11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4!}{4! 4! 2!}$

Step 2.2

Rewrite the expression.

$\frac{11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5}{4! 2!}$

Step 3

Simplify the numerator.

Tap for more steps...

Step 3.1

Multiply $11$ by $10$ .

$\frac{110 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5}{4! 2!}$

Step 3.2

Multiply $110$ by $9$ .

$\frac{990 \cdot 8 \cdot 7 \cdot 6 \cdot 5}{4! 2!}$

Step 3.3

Multiply $990$ by $8$ .

$\frac{7920 \cdot 7 \cdot 6 \cdot 5}{4! 2!}$

Step 3.4

Multiply $7920$ by $7$ .

$\frac{55440 \cdot 6 \cdot 5}{4! 2!}$

Step 3.5

Multiply $55440$ by $6$ .

$\frac{332640 \cdot 5}{4! 2!}$

Step 3.6

Multiply $332640$ by $5$ .

$\frac{1663200}{4! 2!}$

Step 4

Simplify the denominator.

Tap for more steps...

Step 4.1

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

$\frac{1663200}{4 \cdot 3 \cdot 2 \cdot 12!}$

Step 4.2

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

Tap for more steps...

Step 4.2.1

Multiply $4$ by $3$ .

$\frac{1663200}{12 \cdot 2 \cdot 12!}$

Step 4.2.2

Multiply $12$ by $2$ .

$\frac{1663200}{24 \cdot 12!}$

Step 4.2.3

Multiply $24$ by $1$ .

$\frac{1663200}{242!}$

Step 4.3

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

$\frac{1663200}{24 (2 \cdot 1)}$

Step 4.4

Multiply $2$ by $1$ .

$\frac{1663200}{24 \cdot 2}$

Step 5

Simplify the expression.

Tap for more steps...

Step 5.1

Multiply $24$ by $2$ .

$\frac{1663200}{48}$

Step 5.2

Divide $1663200$ by $48$ .

$34650$