Evaluate (11!)/(2!2!2!)

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

Multiply $2!$ by $2!$ .

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

Multiply ${2!}^{2}$ by $2!$ by adding the exponents.

Multiply ${2!}^{2}$ by $2!$ .

Raise $2!$ to the power of $1$ .

$\frac{11!}{{2!}^{2} {2!}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{11!}{{2!}^{2 + 1}}$

Add $2$ and $1$ .

$\frac{11!}{{2!}^{3}}$

Simplify the numerator.

Expand $11!$ to $11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{{2!}^{3}}$

Simplify.

Multiply $11$ by $10$ .

$\frac{110 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{{2!}^{3}}$

Multiply $110$ by $9$ .

$\frac{990 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{{2!}^{3}}$

Multiply $990$ by $8$ .

$\frac{7920 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{{2!}^{3}}$

Multiply $7920$ by $7$ .

$\frac{55440 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{{2!}^{3}}$

Multiply $55440$ by $6$ .

$\frac{332640 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{{2!}^{3}}$

Multiply $332640$ by $5$ .

$\frac{1663200 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{{2!}^{3}}$

Multiply $1663200$ by $4$ .

$\frac{6652800 \cdot 3 \cdot 2 \cdot 1}{{2!}^{3}}$

Multiply $6652800$ by $3$ .

$\frac{19958400 \cdot 2 \cdot 1}{{2!}^{3}}$

Multiply $19958400$ by $2$ .

$\frac{39916800 \cdot 1}{{2!}^{3}}$

Multiply $39916800$ by $1$ .

$\frac{39916800}{{2!}^{3}}$

Simplify the denominator.

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

$\frac{39916800}{{(2 \cdot 1)}^{3}}$

Multiply $2$ by $1$ .

$\frac{39916800}{2^{3}}$

Raise $2$ to the power of $3$ .

$\frac{39916800}{8}$

Divide $39916800$ by $8$ .

$4989600$