Solve 11!/(11-2)!2!*left(.05right)^2*left(.95right)^(11-2)

$$\frac{ 11 ! }{ (11-2) ! 2 ! } \times { \left(.05 \right) }^{ 2 } \times { \left(.95 \right) }^{ (11-2) }$$

Evaluate

$$0.0866592938371337890625$$

Solution Steps

The factorial of 11 is 39916800.

$$\frac{39916800}{\left(11-2\right)!\times 2!}\times 0.05^{2}\times 0.95^{11-2}$$

Subtract 2 from 11 to get 9.

$$\frac{39916800}{9!\times 2!}\times 0.05^{2}\times 0.95^{11-2}$$

The factorial of 9 is 362880.

$$\frac{39916800}{362880\times 2!}\times 0.05^{2}\times 0.95^{11-2}$$

The factorial of 2 is 2.

$$\frac{39916800}{362880\times 2}\times 0.05^{2}\times 0.95^{11-2}$$

Multiply 362880 and 2 to get 725760.

$$\frac{39916800}{725760}\times 0.05^{2}\times 0.95^{11-2}$$

Divide 39916800 by 725760 to get 55.

$$55\times 0.05^{2}\times 0.95^{11-2}$$

Calculate 0.05 to the power of 2 and get 0.0025.

$$55\times 0.0025\times 0.95^{11-2}$$

Multiply 55 and 0.0025 to get 0.1375.

$$0.1375\times 0.95^{11-2}$$

Subtract 2 from 11 to get 9.

$$0.1375\times 0.95^{9}$$

Calculate 0.95 to the power of 9 and get 0.630249409724609375.

$$0.1375\times 0.630249409724609375$$

Multiply 0.1375 and 0.630249409724609375 to get 0.0866592938371337890625.

$$0.0866592938371337890625$$

Factor

$$\frac{11 \cdot 19 ^ {9}}{2 ^ {22} \cdot 5 ^ {10}} = 0.08665929383713379$$