Solve 18!/2!16!0.1^20.9^16

$$\frac{ 18 ! }{ 2 ! 16 ! } { 0.1 }^{ 2 } { 0.9 }^{ 16 }$$

Evaluate

$$0.283512088894331673$$

Solution Steps

The factorial of 18 is 6402373705728000.

$$\frac{6402373705728000}{2!\times 16!}\times 0.1^{2}\times 0.9^{16}$$

The factorial of 2 is 2.

$$\frac{6402373705728000}{2\times 16!}\times 0.1^{2}\times 0.9^{16}$$

The factorial of 16 is 20922789888000.

$$\frac{6402373705728000}{2\times 20922789888000}\times 0.1^{2}\times 0.9^{16}$$

Multiply 2 and 20922789888000 to get 41845579776000.

$$\frac{6402373705728000}{41845579776000}\times 0.1^{2}\times 0.9^{16}$$

Divide 6402373705728000 by 41845579776000 to get 153.

$$153\times 0.1^{2}\times 0.9^{16}$$

Calculate 0.1 to the power of 2 and get 0.01.

$$153\times 0.01\times 0.9^{16}$$

Multiply 153 and 0.01 to get 1.53.

$$1.53\times 0.9^{16}$$

Calculate 0.9 to the power of 16 and get 0.1853020188851841.

$$1.53\times 0.1853020188851841$$

Multiply 1.53 and 0.1853020188851841 to get 0.283512088894331673.

$$0.283512088894331673$$

Factor

$$\frac{17 \cdot 3 ^ {34}}{2 ^ {18} \cdot 5 ^ {18}} = 0.28351208889433166$$