Solve (8!div(2!6!))*0.4^2*left(1-0.4right)^6

$$(8 ! \div (2 ! 6 ! )) \times { 0.4 }^{ 2 } \times { \left(1-0.4 \right) }^{ 6 }$$

Evaluate

$$0.20901888$$

Solution Steps

The factorial of 8 is 40320.

$$\frac{40320}{2!\times 6!}\times 0.4^{2}\left(1-0.4\right)^{6}$$

The factorial of 2 is 2.

$$\frac{40320}{2\times 6!}\times 0.4^{2}\left(1-0.4\right)^{6}$$

The factorial of 6 is 720.

$$\frac{40320}{2\times 720}\times 0.4^{2}\left(1-0.4\right)^{6}$$

Multiply 2 and 720 to get 1440.

$$\frac{40320}{1440}\times 0.4^{2}\left(1-0.4\right)^{6}$$

Divide 40320 by 1440 to get 28.

$$28\times 0.4^{2}\left(1-0.4\right)^{6}$$

Calculate 0.4 to the power of 2 and get 0.16.

$$28\times 0.16\left(1-0.4\right)^{6}$$

Multiply 28 and 0.16 to get 4.48.

$$4.48\left(1-0.4\right)^{6}$$

Subtract 0.4 from 1 to get 0.6.

$$4.48\times 0.6^{6}$$

Calculate 0.6 to the power of 6 and get 0.046656.

$$4.48\times 0.046656$$

Multiply 4.48 and 0.046656 to get 0.20901888.

$$0.20901888$$

Factor

$$\frac{7 \cdot 2 ^ {4} \cdot 3 ^ {6}}{5 ^ {8}} = 0.20901888$$