Solve 5!6!/2!8!

$$\frac { 5 ! 6 ! } { 2 ! 8 ! }$$

Evaluate

$$\frac{15}{14}\approx 1.071428571$$

Solution Steps

The factorial of 5 is 120.

$$\frac{120\times 6!}{2!\times 8!}$$

The factorial of 6 is 720.

$$\frac{120\times 720}{2!\times 8!}$$

Multiply 120 and 720 to get 86400.

$$\frac{86400}{2!\times 8!}$$

The factorial of 2 is 2.

$$\frac{86400}{2\times 8!}$$

The factorial of 8 is 40320.

$$\frac{86400}{2\times 40320}$$

Multiply 2 and 40320 to get 80640.

$$\frac{86400}{80640}$$

Reduce the fraction \frac{86400}{80640} to lowest terms by extracting and canceling out 5760.

$$\frac{15}{14}$$

Factor

$$\frac{3 \cdot 5}{2 \cdot 7} = 1\frac{1}{14} = 1.0714285714285714$$