Resolver 20!/15!5!15!/11!4!

$$\frac{ 20 ! }{ 15 ! 5 ! } \frac{ 15 ! }{ 11 ! 4 ! }$$

Avaliar

$$21162960$$

Passos Para a Resolução

O fatorial de 20 é 2432902008176640000.

$$\frac{2432902008176640000}{15!\times 5!}\times \frac{15!}{11!\times 4!}$$

O fatorial de 15 é 1307674368000.

$$\frac{2432902008176640000}{1307674368000\times 5!}\times \frac{15!}{11!\times 4!}$$

O fatorial de 5 é 120.

$$\frac{2432902008176640000}{1307674368000\times 120}\times \frac{15!}{11!\times 4!}$$

Multiplique 1307674368000 e 120 para obter 156920924160000.

$$\frac{2432902008176640000}{156920924160000}\times \frac{15!}{11!\times 4!}$$

Dividir 2432902008176640000 por 156920924160000 para obter 15504.

$$15504\times \frac{15!}{11!\times 4!}$$

O fatorial de 15 é 1307674368000.

$$15504\times \frac{1307674368000}{11!\times 4!}$$

O fatorial de 11 é 39916800.

$$15504\times \frac{1307674368000}{39916800\times 4!}$$

O fatorial de 4 é 24.

$$15504\times \frac{1307674368000}{39916800\times 24}$$

Multiplique 39916800 e 24 para obter 958003200.

$$15504\times \frac{1307674368000}{958003200}$$

Dividir 1307674368000 por 958003200 para obter 1365.

$$15504\times 1365$$

Multiplique 15504 e 1365 para obter 21162960.

$$21162960$$

Fatorizar

$$2^{4}\times 3^{2}\times 5\times 7\times 13\times 17\times 19$$