Solve =5!/4!(5-4)!0.25^4(0.75)^5-4+5!/5!(5-5)!0.25^5(0.75)^5-5

$$= \frac { 5 ! } { 4 ! ( 5 - 4 ) ! } 0.25 ^ { 4 } ( 0.75 ) ^ { 5 - 4 } + \frac { 5 ! } { 5 ! ( 5 - 5 ) ! } 0.25 ^ { 5 } ( 0.75 ) ^ { 5 - 5 }$$

Evaluate

$$0.015625$$

Solution Steps

The factorial of 5 is 120.

$$\frac{120}{4!\left(5-4\right)!}\times 0.25^{4}\times 0.75^{5-4}+\frac{5!}{5!\left(5-5\right)!}\times 0.25^{5}\times 0.75^{5-5}$$

The factorial of 4 is 24.

$$\frac{120}{24\left(5-4\right)!}\times 0.25^{4}\times 0.75^{5-4}+\frac{5!}{5!\left(5-5\right)!}\times 0.25^{5}\times 0.75^{5-5}$$

Subtract 4 from 5 to get 1.

$$\frac{120}{24\times 1!}\times 0.25^{4}\times 0.75^{5-4}+\frac{5!}{5!\left(5-5\right)!}\times 0.25^{5}\times 0.75^{5-5}$$

The factorial of 1 is 1.

$$\frac{120}{24\times 1}\times 0.25^{4}\times 0.75^{5-4}+\frac{5!}{5!\left(5-5\right)!}\times 0.25^{5}\times 0.75^{5-5}$$

Multiply 24 and 1 to get 24.

$$\frac{120}{24}\times 0.25^{4}\times 0.75^{5-4}+\frac{5!}{5!\left(5-5\right)!}\times 0.25^{5}\times 0.75^{5-5}$$

Divide 120 by 24 to get 5.

$$5\times 0.25^{4}\times 0.75^{5-4}+\frac{5!}{5!\left(5-5\right)!}\times 0.25^{5}\times 0.75^{5-5}$$

Calculate 0.25 to the power of 4 and get 0.00390625.

$$5\times 0.00390625\times 0.75^{5-4}+\frac{5!}{5!\left(5-5\right)!}\times 0.25^{5}\times 0.75^{5-5}$$

Multiply 5 and 0.00390625 to get 0.01953125.

$$0.01953125\times 0.75^{5-4}+\frac{5!}{5!\left(5-5\right)!}\times 0.25^{5}\times 0.75^{5-5}$$

Subtract 4 from 5 to get 1.

$$0.01953125\times 0.75^{1}+\frac{5!}{5!\left(5-5\right)!}\times 0.25^{5}\times 0.75^{5-5}$$

Calculate 0.75 to the power of 1 and get 0.75.

$$0.01953125\times 0.75+\frac{5!}{5!\left(5-5\right)!}\times 0.25^{5}\times 0.75^{5-5}$$

Multiply 0.01953125 and 0.75 to get 0.0146484375.

$$0.0146484375+\frac{5!}{5!\left(5-5\right)!}\times 0.25^{5}\times 0.75^{5-5}$$

The factorial of 5 is 120.

$$0.0146484375+\frac{120}{5!\left(5-5\right)!}\times 0.25^{5}\times 0.75^{5-5}$$

The factorial of 5 is 120.

$$0.0146484375+\frac{120}{120\left(5-5\right)!}\times 0.25^{5}\times 0.75^{5-5}$$

Subtract 5 from 5 to get 0.

$$0.0146484375+\frac{120}{120\times 0!}\times 0.25^{5}\times 0.75^{5-5}$$

The factorial of 0 is 1.

$$0.0146484375+\frac{120}{120\times 1}\times 0.25^{5}\times 0.75^{5-5}$$

Multiply 120 and 1 to get 120.

$$0.0146484375+\frac{120}{120}\times 0.25^{5}\times 0.75^{5-5}$$

Divide 120 by 120 to get 1.

$$0.0146484375+1\times 0.25^{5}\times 0.75^{5-5}$$

Calculate 0.25 to the power of 5 and get 0.0009765625.

$$0.0146484375+1\times 0.0009765625\times 0.75^{5-5}$$

Multiply 1 and 0.0009765625 to get 0.0009765625.

$$0.0146484375+0.0009765625\times 0.75^{5-5}$$

Subtract 5 from 5 to get 0.

$$0.0146484375+0.0009765625\times 0.75^{0}$$

Calculate 0.75 to the power of 0 and get 1.

$$0.0146484375+0.0009765625\times 1$$

Multiply 0.0009765625 and 1 to get 0.0009765625.

$$0.0146484375+0.0009765625$$

Add 0.0146484375 and 0.0009765625 to get 0.015625.

$$0.015625$$

Factor

$$\frac{1}{2 ^ {6}} = 0.015625$$