Solve 7!/0!(7-0)!*0.6^7*0.4^7

$$\frac{ 7 ! }{ 0 ! (7-0) ! } \times { 0.6 }^{ 7 } \times { 0.4 }^{ 7 }$$

Evaluate

$$0.00004586471424$$

Solution Steps

The factorial of 7 is 5040.

$$\frac{5040}{0!\left(7-0\right)!}\times 0.6^{7}\times 0.4^{7}$$

The factorial of 0 is 1.

$$\frac{5040}{1\left(7-0\right)!}\times 0.6^{7}\times 0.4^{7}$$

Subtract 0 from 7 to get 7.

$$\frac{5040}{1\times 7!}\times 0.6^{7}\times 0.4^{7}$$

The factorial of 7 is 5040.

$$\frac{5040}{1\times 5040}\times 0.6^{7}\times 0.4^{7}$$

Multiply 1 and 5040 to get 5040.

$$\frac{5040}{5040}\times 0.6^{7}\times 0.4^{7}$$

Divide 5040 by 5040 to get 1.

$$1\times 0.6^{7}\times 0.4^{7}$$

Calculate 0.6 to the power of 7 and get 0.0279936.

$$1\times 0.0279936\times 0.4^{7}$$

Multiply 1 and 0.0279936 to get 0.0279936.

$$0.0279936\times 0.4^{7}$$

Calculate 0.4 to the power of 7 and get 0.0016384.

$$0.0279936\times 0.0016384$$

Multiply 0.0279936 and 0.0016384 to get 0.00004586471424.

$$0.00004586471424$$

Factor

$$\frac{2 ^ {7} \cdot 3 ^ {7}}{5 ^ {14}} = 4.586471424 \times 10^{-5}$$