Solve (5!*18!)div(4!*17!)

$$(5 ! \times 18 ! ) \div (4 ! \times 17 ! )$$

Evaluate

$$90$$

Solution Steps

The factorial of 5 is 120.

$$\frac{120\times 18!}{4!\times 17!}$$

The factorial of 18 is 6402373705728000.

$$\frac{120\times 6402373705728000}{4!\times 17!}$$

Multiply 120 and 6402373705728000 to get 768284844687360000.

$$\frac{768284844687360000}{4!\times 17!}$$

The factorial of 4 is 24.

$$\frac{768284844687360000}{24\times 17!}$$

The factorial of 17 is 355687428096000.

$$\frac{768284844687360000}{24\times 355687428096000}$$

Multiply 24 and 355687428096000 to get 8536498274304000.

$$\frac{768284844687360000}{8536498274304000}$$

Divide 768284844687360000 by 8536498274304000 to get 90.

$$90$$

Factor

$$2\times 3^{2}\times 5$$