Solve 20!/15!5!15!/11!4!

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

Evaluate

$$21162960$$

Solution Steps

The factorial of 20 is 2432902008176640000.

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

The factorial of 15 is 1307674368000.

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

The factorial of 5 is 120.

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

Multiply 1307674368000 and 120 to get 156920924160000.

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

Divide 2432902008176640000 by 156920924160000 to get 15504.

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

The factorial of 15 is 1307674368000.

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

The factorial of 11 is 39916800.

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

The factorial of 4 is 24.

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

Multiply 39916800 and 24 to get 958003200.

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

Divide 1307674368000 by 958003200 to get 1365.

$$15504\times 1365$$

Multiply 15504 and 1365 to get 21162960.

$$21162960$$

Factor

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