Solve 11!/3!3!2!2!-10!/3!2!2!2!

$$\frac { 11 ! } { 3 ! 3 ! 2 ! 2 ! } - \frac { 10 ! } { 3 ! 2 ! 2 ! 2 ! }$$

Evaluate

$$201600$$

Solution Steps

Multiply 3! and 3! to get \left(3!\right)^{2}.

$$\frac{11!}{\left(3!\right)^{2}\times 2!\times 2!}-\frac{10!}{3!\times 2!\times 2!\times 2!}$$

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

$$\frac{11!}{\left(3!\right)^{2}\times \left(2!\right)^{2}}-\frac{10!}{3!\times 2!\times 2!\times 2!}$$

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

$$\frac{11!}{\left(3!\right)^{2}\times \left(2!\right)^{2}}-\frac{10!}{3!\times \left(2!\right)^{2}\times 2!}$$

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

$$\frac{11!}{\left(3!\right)^{2}\times \left(2!\right)^{2}}-\frac{10!}{3!\times \left(2!\right)^{3}}$$

The factorial of 11 is 39916800.

$$\frac{39916800}{\left(3!\right)^{2}\times \left(2!\right)^{2}}-\frac{10!}{3!\times \left(2!\right)^{3}}$$

The factorial of 3 is 6.

$$\frac{39916800}{6^{2}\times \left(2!\right)^{2}}-\frac{10!}{3!\times \left(2!\right)^{3}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{39916800}{36\times \left(2!\right)^{2}}-\frac{10!}{3!\times \left(2!\right)^{3}}$$

The factorial of 2 is 2.

$$\frac{39916800}{36\times 2^{2}}-\frac{10!}{3!\times \left(2!\right)^{3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{39916800}{36\times 4}-\frac{10!}{3!\times \left(2!\right)^{3}}$$

Multiply 36 and 4 to get 144.

$$\frac{39916800}{144}-\frac{10!}{3!\times \left(2!\right)^{3}}$$

Divide 39916800 by 144 to get 277200.

$$277200-\frac{10!}{3!\times \left(2!\right)^{3}}$$

The factorial of 10 is 3628800.

$$277200-\frac{3628800}{3!\times \left(2!\right)^{3}}$$

The factorial of 3 is 6.

$$277200-\frac{3628800}{6\times \left(2!\right)^{3}}$$

The factorial of 2 is 2.

$$277200-\frac{3628800}{6\times 2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$277200-\frac{3628800}{6\times 8}$$

Multiply 6 and 8 to get 48.

$$277200-\frac{3628800}{48}$$

Divide 3628800 by 48 to get 75600.

$$277200-75600$$

Subtract 75600 from 277200 to get 201600.

$$201600$$

Factor

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