Solve 5!5!/2!7!

$$\frac { 5 ! 5 ! } { 2 ! 7 ! }$$

Evaluate

$$\frac{10}{7}\approx 1.428571429$$

Solution Steps

Multiply 5! and 5! to get \left(5!\right)^{2}.

$$\frac{\left(5!\right)^{2}}{2!\times 7!}$$

The factorial of 5 is 120.

$$\frac{120^{2}}{2!\times 7!}$$

Calculate 120 to the power of 2 and get 14400.

$$\frac{14400}{2!\times 7!}$$

The factorial of 2 is 2.

$$\frac{14400}{2\times 7!}$$

The factorial of 7 is 5040.

$$\frac{14400}{2\times 5040}$$

Multiply 2 and 5040 to get 10080.

$$\frac{14400}{10080}$$

Reduce the fraction \frac{14400}{10080} to lowest terms by extracting and canceling out 1440.

$$\frac{10}{7}$$

Factor

$$\frac{2 \cdot 5}{7} = 1\frac{3}{7} = 1.4285714285714286$$