Solve 14!/7!(14-7)!0.55^7(1-.55)^(14-7)=

$$\frac { 14 ! } { 7 ! ( 14 - 7 ) ! } 0.55 ^ { 7 } ( 1 - .55 ) ^ { ( 14 - 7 ) } =$$

Evaluate

$$0.1952422042246575732421875$$

Solution Steps

The factorial of 14 is 87178291200.

$$\frac{87178291200}{7!\left(14-7\right)!}\times 0.55^{7}\left(1-0.55\right)^{14-7}$$

The factorial of 7 is 5040.

$$\frac{87178291200}{5040\left(14-7\right)!}\times 0.55^{7}\left(1-0.55\right)^{14-7}$$

Subtract 7 from 14 to get 7.

$$\frac{87178291200}{5040\times 7!}\times 0.55^{7}\left(1-0.55\right)^{14-7}$$

The factorial of 7 is 5040.

$$\frac{87178291200}{5040\times 5040}\times 0.55^{7}\left(1-0.55\right)^{14-7}$$

Multiply 5040 and 5040 to get 25401600.

$$\frac{87178291200}{25401600}\times 0.55^{7}\left(1-0.55\right)^{14-7}$$

Divide 87178291200 by 25401600 to get 3432.

$$3432\times 0.55^{7}\left(1-0.55\right)^{14-7}$$

Calculate 0.55 to the power of 7 and get 0.01522435234375.

$$3432\times 0.01522435234375\left(1-0.55\right)^{14-7}$$

Multiply 3432 and 0.01522435234375 to get 52.24997724375.

$$52.24997724375\left(1-0.55\right)^{14-7}$$

Subtract 0.55 from 1 to get 0.45.

$$52.24997724375\times 0.45^{14-7}$$

Subtract 7 from 14 to get 7.

$$52.24997724375\times 0.45^{7}$$

Calculate 0.45 to the power of 7 and get 0.00373669453125.

$$52.24997724375\times 0.00373669453125$$

Multiply 52.24997724375 and 0.00373669453125 to get 0.1952422042246575732421875.

$$0.1952422042246575732421875$$

Factor

$$\frac{13 \cdot 3 ^ {15} \cdot 11 ^ {8}}{2 ^ {25} \cdot 5 ^ {14}} = 0.19524220422465757$$