Solve 10!6!/7!9!

$$\frac { 10 ! 6 ! } { 7 ! 9 ! }$$

Evaluate

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

Solution Steps

The factorial of 10 is 3628800.

$$\frac{3628800\times 6!}{7!\times 9!}$$

The factorial of 6 is 720.

$$\frac{3628800\times 720}{7!\times 9!}$$

Multiply 3628800 and 720 to get 2612736000.

$$\frac{2612736000}{7!\times 9!}$$

The factorial of 7 is 5040.

$$\frac{2612736000}{5040\times 9!}$$

The factorial of 9 is 362880.

$$\frac{2612736000}{5040\times 362880}$$

Multiply 5040 and 362880 to get 1828915200.

$$\frac{2612736000}{1828915200}$$

Reduce the fraction \frac{2612736000}{1828915200} to lowest terms by extracting and canceling out 261273600.

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

Factor

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