Solve 7!/2!4!3!

$$\frac { 7 ! } { 2 ! 4 ! 3 ! }$$

Evaluate

$$\frac{35}{2}=17.5$$

Solution Steps

The factorial of 7 is 5040.

$$\frac{5040}{2!\times 4!\times 3!}$$

The factorial of 2 is 2.

$$\frac{5040}{2\times 4!\times 3!}$$

The factorial of 4 is 24.

$$\frac{5040}{2\times 24\times 3!}$$

Multiply 2 and 24 to get 48.

$$\frac{5040}{48\times 3!}$$

The factorial of 3 is 6.

$$\frac{5040}{48\times 6}$$

Multiply 48 and 6 to get 288.

$$\frac{5040}{288}$$

Reduce the fraction \frac{5040}{288} to lowest terms by extracting and canceling out 144.

$$\frac{35}{2}$$

Factor

$$\frac{5 \cdot 7}{2} = 17\frac{1}{2} = 17.5$$