Solve 6!7!/4!9!

$$\frac { 6 ! 7 ! } { 4 ! 9 ! }$$

Evaluate

$$\frac{5}{12}\approx 0.416666667$$

Solution Steps

The factorial of 6 is 720.

$$\frac{720\times 7!}{4!\times 9!}$$

The factorial of 7 is 5040.

$$\frac{720\times 5040}{4!\times 9!}$$

Multiply 720 and 5040 to get 3628800.

$$\frac{3628800}{4!\times 9!}$$

The factorial of 4 is 24.

$$\frac{3628800}{24\times 9!}$$

The factorial of 9 is 362880.

$$\frac{3628800}{24\times 362880}$$

Multiply 24 and 362880 to get 8709120.

$$\frac{3628800}{8709120}$$

Reduce the fraction \frac{3628800}{8709120} to lowest terms by extracting and canceling out 725760.

$$\frac{5}{12}$$

Factor

$$\frac{5}{2 ^ {2} \cdot 3} = 0.4166666666666667$$