Solve 1!1!/21!

$$\frac { 1 ! 1 ! } { 21 ! }$$

Evaluate

$$\frac{1}{51090942171709440000}\approx 1.957294106 \cdot 10^{-20}$$

Solution Steps

Multiply 1! and 1! to get \left(1!\right)^{2}.

$$\frac{\left(1!\right)^{2}}{21!}$$

The factorial of 1 is 1.

$$\frac{1^{2}}{21!}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{1}{21!}$$

The factorial of 21 is 51090942171709440000.

$$\frac{1}{51090942171709440000}$$

Factor

$$\frac{1}{2 ^ {18} \cdot 3 ^ {9} \cdot 5 ^ {4} \cdot 7 ^ {3} \cdot 11 \cdot 13 \cdot 17 \cdot 19} = 1.9572941063391263 \times 10^{-20}$$