Solve 11!/2!2!2!

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

Evaluate

$$4989600$$

Solution Steps

Multiply 2! and 2! to get \left(2!\right)^{2}.

$$\frac{11!}{\left(2!\right)^{2}\times 2!}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{11!}{\left(2!\right)^{3}}$$

The factorial of 11 is 39916800.

$$\frac{39916800}{\left(2!\right)^{3}}$$

The factorial of 2 is 2.

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

Calculate 2 to the power of 3 and get 8.

$$\frac{39916800}{8}$$

Divide 39916800 by 8 to get 4989600.

$$4989600$$

Factor

$$2^{5}\times 3^{4}\times 5^{2}\times 7\times 11$$