Solve 20!/5!10!3!

$$\frac { 20 ! } { 5 ! 10 ! 3 ! }$$

Evaluate

$$931170240$$

Solution Steps

The factorial of 20 is 2432902008176640000.

$$\frac{2432902008176640000}{5!\times 10!\times 3!}$$

The factorial of 5 is 120.

$$\frac{2432902008176640000}{120\times 10!\times 3!}$$

The factorial of 10 is 3628800.

$$\frac{2432902008176640000}{120\times 3628800\times 3!}$$

Multiply 120 and 3628800 to get 435456000.

$$\frac{2432902008176640000}{435456000\times 3!}$$

The factorial of 3 is 6.

$$\frac{2432902008176640000}{435456000\times 6}$$

Multiply 435456000 and 6 to get 2612736000.

$$\frac{2432902008176640000}{2612736000}$$

Divide 2432902008176640000 by 2612736000 to get 931170240.

$$931170240$$

Factor

$$2^{6}\times 3^{2}\times 5\times 7\times 11\times 13\times 17\times 19$$