Solve 1-{left(5!-1/5!right)}^7

$$1- { \left( \frac{ 5 ! -1 }{ 5 ! } \right) }^{ 7 }$$

Evaluate

$$\frac{20386538221561}{358318080000000}\approx 0.056895087$$

Solution Steps

The factorial of 5 is 120.

$$1-\left(\frac{120-1}{5!}\right)^{7}$$

Subtract 1 from 120 to get 119.

$$1-\left(\frac{119}{5!}\right)^{7}$$

The factorial of 5 is 120.

$$1-\left(\frac{119}{120}\right)^{7}$$

Calculate \frac{119}{120} to the power of 7 and get \frac{337931541778439}{358318080000000}.

$$1-\frac{337931541778439}{358318080000000}$$

Subtract \frac{337931541778439}{358318080000000} from 1 to get \frac{20386538221561}{358318080000000}.

$$\frac{20386538221561}{358318080000000}$$

Factor

$$\frac{20386538221561}{2 ^ {21} \cdot 3 ^ {7} \cdot 5 ^ {7}} = 0.05689508668265079$$