Solve 25!/(25-6)!6!

$$\frac { 25 ! } { ( 25 - 6 ) ! 6 ! }$$

Evaluate

$$177100$$

Solution Steps

The factorial of 25 is 15511210043330985984000000.

$$\frac{15511210043330985984000000}{\left(25-6\right)!\times 6!}$$

Subtract 6 from 25 to get 19.

$$\frac{15511210043330985984000000}{19!\times 6!}$$

The factorial of 19 is 121645100408832000.

$$\frac{15511210043330985984000000}{121645100408832000\times 6!}$$

The factorial of 6 is 720.

$$\frac{15511210043330985984000000}{121645100408832000\times 720}$$

Multiply 121645100408832000 and 720 to get 87584472294359040000.

$$\frac{15511210043330985984000000}{87584472294359040000}$$

Divide 15511210043330985984000000 by 87584472294359040000 to get 177100.

$$177100$$

Factor

$$2^{2}\times 5^{2}\times 7\times 11\times 23$$