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

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

Baholash

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

Yechim qadamlari

30 ning faktoriali 265252859812191058636308480000000 ga teng.

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

4 ning faktoriali 24 ga teng.

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

11052202492174627443179520000000 ni olish uchun 265252859812191058636308480000000 ni 24 ga bo‘ling.

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

26 ning faktoriali 403291461126605635584000000 ga teng.

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

27405 ni olish uchun 11052202492174627443179520000000 ni 403291461126605635584000000 ga bo‘ling.

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

274050 hosil qilish uchun 27405 va 10 ni ko'paytirish.

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

40 ning faktoriali 815915283247897734345611269596115894272000000000 ga teng.

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

5 ning faktoriali 120 ga teng.

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

6799294027065814452880093913300965785600000000 ni olish uchun 815915283247897734345611269596115894272000000000 ni 120 ga bo‘ling.

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

35 ning faktoriali 10333147966386144929666651337523200000000 ga teng.

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

658008 ni olish uchun 6799294027065814452880093913300965785600000000 ni 10333147966386144929666651337523200000000 ga bo‘ling.

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

\frac{274050}{658008} ulushini 18 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

Omil

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