Solve 20!/2!(20!-2!)

$$\frac { 20 ! } { 2 ! ( 20 ! - 2 ! ) }$$

Evaluate

$$\frac{608225502044160000}{1216451004088319999}\approx 0.5$$

Solution Steps

The factorial of 20 is 2432902008176640000.

$$\frac{2432902008176640000}{2!\left(20!-2!\right)}$$

The factorial of 2 is 2.

$$\frac{2432902008176640000}{2\left(20!-2!\right)}$$

The factorial of 20 is 2432902008176640000.

$$\frac{2432902008176640000}{2\left(2432902008176640000-2!\right)}$$

The factorial of 2 is 2.

$$\frac{2432902008176640000}{2\left(2432902008176640000-2\right)}$$

Subtract 2 from 2432902008176640000 to get 2432902008176639998.

$$\frac{2432902008176640000}{2\times 2432902008176639998}$$

Multiply 2 and 2432902008176639998 to get 4865804016353279996.

$$\frac{2432902008176640000}{4865804016353279996}$$

Reduce the fraction \frac{2432902008176640000}{4865804016353279996} to lowest terms by extracting and canceling out 4.

$$\frac{608225502044160000}{1216451004088319999}$$

Factor

$$\frac{2 ^ {16} \cdot 3 ^ {8} \cdot 5 ^ {4} \cdot 7 ^ {2} \cdot 11 \cdot 13 \cdot 17 \cdot 19}{43 \cdot 1451 \cdot 1559 \cdot 12505833377} = 0.5$$