Solve 11!/3!3!2!2!-9!/3!3!

$$\frac { 11 ! } { 3 ! 3 ! 2 ! 2 ! } - \frac { 9 ! } { 3 ! 3 ! }$$

Evaluate

$$267120$$

Solution Steps

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

$$\frac{11!}{\left(3!\right)^{2}\times 2!\times 2!}-\frac{9!}{3!\times 3!}$$

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

$$\frac{11!}{\left(3!\right)^{2}\times \left(2!\right)^{2}}-\frac{9!}{3!\times 3!}$$

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

$$\frac{11!}{\left(3!\right)^{2}\times \left(2!\right)^{2}}-\frac{9!}{\left(3!\right)^{2}}$$

The factorial of 11 is 39916800.

$$\frac{39916800}{\left(3!\right)^{2}\times \left(2!\right)^{2}}-\frac{9!}{\left(3!\right)^{2}}$$

The factorial of 3 is 6.

$$\frac{39916800}{6^{2}\times \left(2!\right)^{2}}-\frac{9!}{\left(3!\right)^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{39916800}{36\times \left(2!\right)^{2}}-\frac{9!}{\left(3!\right)^{2}}$$

The factorial of 2 is 2.

$$\frac{39916800}{36\times 2^{2}}-\frac{9!}{\left(3!\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{39916800}{36\times 4}-\frac{9!}{\left(3!\right)^{2}}$$

Multiply 36 and 4 to get 144.

$$\frac{39916800}{144}-\frac{9!}{\left(3!\right)^{2}}$$

Divide 39916800 by 144 to get 277200.

$$277200-\frac{9!}{\left(3!\right)^{2}}$$

The factorial of 9 is 362880.

$$277200-\frac{362880}{\left(3!\right)^{2}}$$

The factorial of 3 is 6.

$$277200-\frac{362880}{6^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$277200-\frac{362880}{36}$$

Divide 362880 by 36 to get 10080.

$$277200-10080$$

Subtract 10080 from 277200 to get 267120.

$$267120$$

Factor

$$2^{4}\times 3^{2}\times 5\times 7\times 53$$