Lutasin ang 30!div4!div26!*10/40!div5!div35!

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

I-evaluate

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

Mga Hakbang ng Solution

Ang factorial ng 30 ay 265252859812191058636308480000000.

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

Ang factorial ng 4 ay 24.

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

I-divide ang 265252859812191058636308480000000 gamit ang 24 para makuha ang 11052202492174627443179520000000.

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

Ang factorial ng 26 ay 403291461126605635584000000.

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

I-divide ang 11052202492174627443179520000000 gamit ang 403291461126605635584000000 para makuha ang 27405.

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

I-multiply ang 27405 at 10 para makuha ang 274050.

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

Ang factorial ng 40 ay 815915283247897734345611269596115894272000000000.

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

Ang factorial ng 5 ay 120.

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

I-divide ang 815915283247897734345611269596115894272000000000 gamit ang 120 para makuha ang 6799294027065814452880093913300965785600000000.

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

Ang factorial ng 35 ay 10333147966386144929666651337523200000000.

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

I-divide ang 6799294027065814452880093913300965785600000000 gamit ang 10333147966386144929666651337523200000000 para makuha ang 658008.

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

Bawasan ang fraction \frac{274050}{658008} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 18.

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

I-factor

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