Solve 30!div4!div26!*10/40!div5!div35!

$$\frac{ 30 ! \div 4 ! \div 26 ! \times 10 }{ 40 ! \div 5 ! \div 35 ! }$$

Evaluate

$$\frac{15225}{36556}\approx 0.416484298$$

Solution Steps

The factorial of 30 is 265252859812191058636308480000000.

$$\frac{\frac{\frac{265252859812191058636308480000000}{4!}}{26!}\times 10}{\frac{\frac{40!}{5!}}{35!}}$$

The factorial of 4 is 24.

$$\frac{\frac{\frac{265252859812191058636308480000000}{24}}{26!}\times 10}{\frac{\frac{40!}{5!}}{35!}}$$

Divide 265252859812191058636308480000000 by 24 to get 11052202492174627443179520000000.

$$\frac{\frac{11052202492174627443179520000000}{26!}\times 10}{\frac{\frac{40!}{5!}}{35!}}$$

The factorial of 26 is 403291461126605635584000000.

$$\frac{\frac{11052202492174627443179520000000}{403291461126605635584000000}\times 10}{\frac{\frac{40!}{5!}}{35!}}$$

Divide 11052202492174627443179520000000 by 403291461126605635584000000 to get 27405.

$$\frac{27405\times 10}{\frac{\frac{40!}{5!}}{35!}}$$

Multiply 27405 and 10 to get 274050.

$$\frac{274050}{\frac{\frac{40!}{5!}}{35!}}$$

The factorial of 40 is 815915283247897734345611269596115894272000000000.

$$\frac{274050}{\frac{\frac{815915283247897734345611269596115894272000000000}{5!}}{35!}}$$

The factorial of 5 is 120.

$$\frac{274050}{\frac{\frac{815915283247897734345611269596115894272000000000}{120}}{35!}}$$

Divide 815915283247897734345611269596115894272000000000 by 120 to get 6799294027065814452880093913300965785600000000.

$$\frac{274050}{\frac{6799294027065814452880093913300965785600000000}{35!}}$$

The factorial of 35 is 10333147966386144929666651337523200000000.

$$\frac{274050}{\frac{6799294027065814452880093913300965785600000000}{10333147966386144929666651337523200000000}}$$

Divide 6799294027065814452880093913300965785600000000 by 10333147966386144929666651337523200000000 to get 658008.

$$\frac{274050}{658008}$$

Reduce the fraction \frac{274050}{658008} to lowest terms by extracting and canceling out 18.

$$\frac{15225}{36556}$$

Factor

$$\frac{3 \cdot 5 ^ {2} \cdot 7 \cdot 29}{2 ^ {2} \cdot 13 \cdot 19 \cdot 37} = 0.41648429806324544$$