Solve 24!/5!(9)!

$$\frac { 24 ! } { 5 ! ( 9 ) ! }$$

Evaluate

$$14248245557145600$$

Solution Steps

The factorial of 24 is 620448401733239439360000.

$$\frac{620448401733239439360000}{5!\times 9!}$$

The factorial of 5 is 120.

$$\frac{620448401733239439360000}{120\times 9!}$$

The factorial of 9 is 362880.

$$\frac{620448401733239439360000}{120\times 362880}$$

Multiply 120 and 362880 to get 43545600.

$$\frac{620448401733239439360000}{43545600}$$

Divide 620448401733239439360000 by 43545600 to get 14248245557145600.

$$14248245557145600$$

Factor

$$2^{12}\times 3^{5}\times 5^{2}\times 7^{2}\times 11^{2}\times 13\times 17\times 19\times 23$$