Solve 5!4!/7!2!

$$\frac { 5 ! 4 ! } { 7 ! 2 ! }$$

Evaluate

$$\frac{2}{7}\approx 0.285714286$$

Solution Steps

The factorial of 5 is 120.

$$\frac{120\times 4!}{7!\times 2!}$$

The factorial of 4 is 24.

$$\frac{120\times 24}{7!\times 2!}$$

Multiply 120 and 24 to get 2880.

$$\frac{2880}{7!\times 2!}$$

The factorial of 7 is 5040.

$$\frac{2880}{5040\times 2!}$$

The factorial of 2 is 2.

$$\frac{2880}{5040\times 2}$$

Multiply 5040 and 2 to get 10080.

$$\frac{2880}{10080}$$

Reduce the fraction \frac{2880}{10080} to lowest terms by extracting and canceling out 1440.

$$\frac{2}{7}$$

Factor

$$\frac{2}{7} = 0.2857142857142857$$