Solve 16!/4!(16-4)!

$$\frac { 16 ! } { 4 ! ( 16 - 4 ) ! }$$

Evaluate

$$1820$$

Solution Steps

The factorial of 16 is 20922789888000.

$$\frac{20922789888000}{4!\left(16-4\right)!}$$

The factorial of 4 is 24.

$$\frac{20922789888000}{24\left(16-4\right)!}$$

Subtract 4 from 16 to get 12.

$$\frac{20922789888000}{24\times 12!}$$

The factorial of 12 is 479001600.

$$\frac{20922789888000}{24\times 479001600}$$

Multiply 24 and 479001600 to get 11496038400.

$$\frac{20922789888000}{11496038400}$$

Divide 20922789888000 by 11496038400 to get 1820.

$$1820$$

Factor

$$2^{2}\times 5\times 7\times 13$$