Solve 6!3!/4!7!

$$\frac{ 6 ! 3 ! }{ 4 ! 7 ! }$$

Evaluate

$$\frac{1}{28}\approx 0.035714286$$

Solution Steps

The factorial of 6 is 720.

$$\frac{720\times 3!}{4!\times 7!}$$

The factorial of 3 is 6.

$$\frac{720\times 6}{4!\times 7!}$$

Multiply 720 and 6 to get 4320.

$$\frac{4320}{4!\times 7!}$$

The factorial of 4 is 24.

$$\frac{4320}{24\times 7!}$$

The factorial of 7 is 5040.

$$\frac{4320}{24\times 5040}$$

Multiply 24 and 5040 to get 120960.

$$\frac{4320}{120960}$$

Reduce the fraction \frac{4320}{120960} to lowest terms by extracting and canceling out 4320.

$$\frac{1}{28}$$

Factor

$$\frac{1}{2 ^ {2} \cdot 7} = 0.03571428571428571$$