Solve 12!/(3!)^2(6!)^2

$$\frac { 12 ! } { ( 3 ! ) ^ { 2 } ( 6 ! ) ^ { 2 } }$$

Evaluate

$$\frac{77}{3}\approx 25.666666667$$

Solution Steps

The factorial of 12 is 479001600.

$$\frac{479001600}{\left(3!\right)^{2}\times \left(6!\right)^{2}}$$

The factorial of 3 is 6.

$$\frac{479001600}{6^{2}\times \left(6!\right)^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{479001600}{36\times \left(6!\right)^{2}}$$

The factorial of 6 is 720.

$$\frac{479001600}{36\times 720^{2}}$$

Calculate 720 to the power of 2 and get 518400.

$$\frac{479001600}{36\times 518400}$$

Multiply 36 and 518400 to get 18662400.

$$\frac{479001600}{18662400}$$

Reduce the fraction \frac{479001600}{18662400} to lowest terms by extracting and canceling out 6220800.

$$\frac{77}{3}$$

Factor

$$\frac{7 \cdot 11}{3} = 25\frac{2}{3} = 25.666666666666668$$