Solve 16!/(8!(16-8)!)

$$\frac{ 16 ! }{ (8 ! (16-8) ! ) }$$

Evaluate

$$12870$$

Solution Steps

The factorial of 16 is 20922789888000.

$$\frac{20922789888000}{8!\left(16-8\right)!}$$

The factorial of 8 is 40320.

$$\frac{20922789888000}{40320\left(16-8\right)!}$$

Subtract 8 from 16 to get 8.

$$\frac{20922789888000}{40320\times 8!}$$

The factorial of 8 is 40320.

$$\frac{20922789888000}{40320\times 40320}$$

Multiply 40320 and 40320 to get 1625702400.

$$\frac{20922789888000}{1625702400}$$

Divide 20922789888000 by 1625702400 to get 12870.

$$12870$$

Factor

$$2\times 3^{2}\times 5\times 11\times 13$$