Ratkaise 20!/15!5!15!/11!4!

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

Laske

$$21162960$$

Ratkaisun vaiheet

20:n kertoma on 2432902008176640000.

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

15:n kertoma on 1307674368000.

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

5:n kertoma on 120.

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

Kerro 1307674368000 ja 120, niin saadaan 156920924160000.

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

Jaa 2432902008176640000 luvulla 156920924160000, jolloin ratkaisuksi tulee 15504.

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

15:n kertoma on 1307674368000.

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

11:n kertoma on 39916800.

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

4:n kertoma on 24.

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

Kerro 39916800 ja 24, niin saadaan 958003200.

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

Jaa 1307674368000 luvulla 958003200, jolloin ratkaisuksi tulee 1365.

$$15504\times 1365$$

Kerro 15504 ja 1365, niin saadaan 21162960.

$$21162960$$

Jaa tekijöihin

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