Solve 40!/20!20!2^40

$$\frac { 40 ! } { 20 ! 20 ! 2 ^ { 40 } }$$

Evaluate

$$\frac{34461632205}{274877906944}\approx 0.125370688$$

Solution Steps

Multiply 20! and 20! to get \left(20!\right)^{2}.

$$\frac{40!}{\left(20!\right)^{2}\times 2^{40}}$$

The factorial of 40 is 815915283247897734345611269596115894272000000000.

$$\frac{815915283247897734345611269596115894272000000000}{\left(20!\right)^{2}\times 2^{40}}$$

The factorial of 20 is 2432902008176640000.

$$\frac{815915283247897734345611269596115894272000000000}{2432902008176640000^{2}\times 2^{40}}$$

Calculate 2432902008176640000 to the power of 2 and get 5919012181389927685417441689600000000.

$$\frac{815915283247897734345611269596115894272000000000}{5919012181389927685417441689600000000\times 2^{40}}$$

Calculate 2 to the power of 40 and get 1099511627776.

$$\frac{815915283247897734345611269596115894272000000000}{5919012181389927685417441689600000000\times 1099511627776}$$

Multiply 5919012181389927685417441689600000000 and 1099511627776 to get 6508022718386011963564259370193659730329600000000.

$$\frac{815915283247897734345611269596115894272000000000}{6508022718386011963564259370193659730329600000000}$$

Reduce the fraction \frac{815915283247897734345611269596115894272000000000}{6508022718386011963564259370193659730329600000000} to lowest terms by extracting and canceling out 23676048725559710741669766758400000000.

$$\frac{34461632205}{274877906944}$$

Factor

$$\frac{3 ^ {2} \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 23 \cdot 29 \cdot 31 \cdot 37}{2 ^ {38}} = 0.12537068761957926$$