Solve 6!/(6-3)!3!*left(.167right)^3*left(.833right)^(6-3)

$$\frac{ 6 ! }{ (6-3) ! 3 ! } \times { \left(.167 \right) }^{ 3 } \times { \left(.833 \right) }^{ (6-3) }$$

Evaluate

$$0.05384116064449262$$

Solution Steps

The factorial of 6 is 720.

$$\frac{720}{\left(6-3\right)!\times 3!}\times 0.167^{3}\times 0.833^{6-3}$$

Subtract 3 from 6 to get 3.

$$\frac{720}{3!\times 3!}\times 0.167^{3}\times 0.833^{6-3}$$

The factorial of 3 is 6.

$$\frac{720}{6\times 3!}\times 0.167^{3}\times 0.833^{6-3}$$

The factorial of 3 is 6.

$$\frac{720}{6\times 6}\times 0.167^{3}\times 0.833^{6-3}$$

Multiply 6 and 6 to get 36.

$$\frac{720}{36}\times 0.167^{3}\times 0.833^{6-3}$$

Divide 720 by 36 to get 20.

$$20\times 0.167^{3}\times 0.833^{6-3}$$

Calculate 0.167 to the power of 3 and get 0.004657463.

$$20\times 0.004657463\times 0.833^{6-3}$$

Multiply 20 and 0.004657463 to get 0.09314926.

$$0.09314926\times 0.833^{6-3}$$

Subtract 3 from 6 to get 3.

$$0.09314926\times 0.833^{3}$$

Calculate 0.833 to the power of 3 and get 0.578009537.

$$0.09314926\times 0.578009537$$

Multiply 0.09314926 and 0.578009537 to get 0.05384116064449262.

$$0.05384116064449262$$

Factor

$$\frac{7 ^ {6} \cdot 17 ^ {3} \cdot 167 ^ {3}}{2 ^ {16} \cdot 5 ^ {17}} = 0.05384116064449262$$