Solve 21!/2!19!*3!/2!

$$\frac { 21 ! } { 2 ! 19 ! } \times \frac { 3 ! } { 2 ! }$$

Evaluate

$$630$$

Solution Steps

The factorial of 21 is 51090942171709440000.

$$\frac{51090942171709440000}{2!\times 19!}\times \frac{3!}{2!}$$

The factorial of 2 is 2.

$$\frac{51090942171709440000}{2\times 19!}\times \frac{3!}{2!}$$

The factorial of 19 is 121645100408832000.

$$\frac{51090942171709440000}{2\times 121645100408832000}\times \frac{3!}{2!}$$

Multiply 2 and 121645100408832000 to get 243290200817664000.

$$\frac{51090942171709440000}{243290200817664000}\times \frac{3!}{2!}$$

Divide 51090942171709440000 by 243290200817664000 to get 210.

$$210\times \frac{3!}{2!}$$

The factorial of 3 is 6.

$$210\times \frac{6}{2!}$$

The factorial of 2 is 2.

$$210\times \frac{6}{2}$$

Divide 6 by 2 to get 3.

$$210\times 3$$

Multiply 210 and 3 to get 630.

$$630$$

Factor

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