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

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

Procijeni

$$\frac{15225}{36556}\approx 0,416484298$$

Koraci za rješenje

Faktorijel od 30 je 265252859812191058636308480000000.

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

Faktorijel od 4 je 24.

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

Podijelite 265252859812191058636308480000000 sa 24 da biste dobili 11052202492174627443179520000000.

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

Faktorijel od 26 je 403291461126605635584000000.

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

Podijelite 11052202492174627443179520000000 sa 403291461126605635584000000 da biste dobili 27405.

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

Pomnožite 27405 i 10 da biste dobili 274050.

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

Faktorijel od 40 je 815915283247897734345611269596115894272000000000.

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

Faktorijel od 5 je 120.

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

Podijelite 815915283247897734345611269596115894272000000000 sa 120 da biste dobili 6799294027065814452880093913300965785600000000.

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

Faktorijel od 35 je 10333147966386144929666651337523200000000.

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

Podijelite 6799294027065814452880093913300965785600000000 sa 10333147966386144929666651337523200000000 da biste dobili 658008.

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

Svedite razlomak \frac{274050}{658008} na najprostije elemente rastavlјanjem i kraćenjem 18.

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

Faktor

$$\frac{3 \cdot 5 ^ {2} \cdot 7 \cdot 29}{2 ^ {2} \cdot 13 \cdot 19 \cdot 37} = 0,41648429806324544$$