Solve 30!div2!div28!*(10!div3!div7!)/40!div5!div35!

$$\frac{ 30 ! \div 2 ! \div 28 ! \times (10 ! \div 3 ! \div 7 ! ) }{ 40 ! \div 5 ! \div 35 ! }$$

Evaluate

$$\frac{725}{9139}\approx 0.079330342$$

Solution Steps

The factorial of 30 is 265252859812191058636308480000000.

$$\frac{\frac{\frac{265252859812191058636308480000000}{2!}}{28!}\times \frac{\frac{10!}{3!}}{7!}}{\frac{\frac{40!}{5!}}{35!}}$$

The factorial of 2 is 2.

$$\frac{\frac{\frac{265252859812191058636308480000000}{2}}{28!}\times \frac{\frac{10!}{3!}}{7!}}{\frac{\frac{40!}{5!}}{35!}}$$

Divide 265252859812191058636308480000000 by 2 to get 132626429906095529318154240000000.

$$\frac{\frac{132626429906095529318154240000000}{28!}\times \frac{\frac{10!}{3!}}{7!}}{\frac{\frac{40!}{5!}}{35!}}$$

The factorial of 28 is 304888344611713860501504000000.

$$\frac{\frac{132626429906095529318154240000000}{304888344611713860501504000000}\times \frac{\frac{10!}{3!}}{7!}}{\frac{\frac{40!}{5!}}{35!}}$$

Divide 132626429906095529318154240000000 by 304888344611713860501504000000 to get 435.

$$\frac{435\times \frac{\frac{10!}{3!}}{7!}}{\frac{\frac{40!}{5!}}{35!}}$$

The factorial of 10 is 3628800.

$$\frac{435\times \frac{\frac{3628800}{3!}}{7!}}{\frac{\frac{40!}{5!}}{35!}}$$

The factorial of 3 is 6.

$$\frac{435\times \frac{\frac{3628800}{6}}{7!}}{\frac{\frac{40!}{5!}}{35!}}$$

Divide 3628800 by 6 to get 604800.

$$\frac{435\times \frac{604800}{7!}}{\frac{\frac{40!}{5!}}{35!}}$$

The factorial of 7 is 5040.

$$\frac{435\times \frac{604800}{5040}}{\frac{\frac{40!}{5!}}{35!}}$$

Divide 604800 by 5040 to get 120.

$$\frac{435\times 120}{\frac{\frac{40!}{5!}}{35!}}$$

Multiply 435 and 120 to get 52200.

$$\frac{52200}{\frac{\frac{40!}{5!}}{35!}}$$

The factorial of 40 is 815915283247897734345611269596115894272000000000.

$$\frac{52200}{\frac{\frac{815915283247897734345611269596115894272000000000}{5!}}{35!}}$$

The factorial of 5 is 120.

$$\frac{52200}{\frac{\frac{815915283247897734345611269596115894272000000000}{120}}{35!}}$$

Divide 815915283247897734345611269596115894272000000000 by 120 to get 6799294027065814452880093913300965785600000000.

$$\frac{52200}{\frac{6799294027065814452880093913300965785600000000}{35!}}$$

The factorial of 35 is 10333147966386144929666651337523200000000.

$$\frac{52200}{\frac{6799294027065814452880093913300965785600000000}{10333147966386144929666651337523200000000}}$$

Divide 6799294027065814452880093913300965785600000000 by 10333147966386144929666651337523200000000 to get 658008.

$$\frac{52200}{658008}$$

Reduce the fraction \frac{52200}{658008} to lowest terms by extracting and canceling out 72.

$$\frac{725}{9139}$$

Factor

$$\frac{5 ^ {2} \cdot 29}{13 \cdot 19 \cdot 37} = 0.07933034248823723$$