Solve 12!11!/9!10!

$$\frac { 12 ! 11 ! } { 9 ! 10 ! }$$

Evaluate

$$14520$$

Solution Steps

The factorial of 12 is 479001600.

$$\frac{479001600\times 11!}{9!\times 10!}$$

The factorial of 11 is 39916800.

$$\frac{479001600\times 39916800}{9!\times 10!}$$

Multiply 479001600 and 39916800 to get 19120211066880000.

$$\frac{19120211066880000}{9!\times 10!}$$

The factorial of 9 is 362880.

$$\frac{19120211066880000}{362880\times 10!}$$

The factorial of 10 is 3628800.

$$\frac{19120211066880000}{362880\times 3628800}$$

Multiply 362880 and 3628800 to get 1316818944000.

$$\frac{19120211066880000}{1316818944000}$$

Divide 19120211066880000 by 1316818944000 to get 14520.

$$14520$$

Factor

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