Solve =4!/(4-2)!*7!/(7-4)!

$$= \frac { 4 ! } { ( 4 - 2 ) ! } \times \frac { 7 ! } { ( 7 - 4 ) ! }$$

Evaluate

$$10080$$

Solution Steps

The factorial of 4 is 24.

$$\frac{24}{\left(4-2\right)!}\times \frac{7!}{\left(7-4\right)!}$$

Subtract 2 from 4 to get 2.

$$\frac{24}{2!}\times \frac{7!}{\left(7-4\right)!}$$

The factorial of 2 is 2.

$$\frac{24}{2}\times \frac{7!}{\left(7-4\right)!}$$

Divide 24 by 2 to get 12.

$$12\times \frac{7!}{\left(7-4\right)!}$$

The factorial of 7 is 5040.

$$12\times \frac{5040}{\left(7-4\right)!}$$

Subtract 4 from 7 to get 3.

$$12\times \frac{5040}{3!}$$

The factorial of 3 is 6.

$$12\times \frac{5040}{6}$$

Divide 5040 by 6 to get 840.

$$12\times 840$$

Multiply 12 and 840 to get 10080.

$$10080$$

Factor

$$2^{5}\times 3^{2}\times 5\times 7$$