Solve 15!/12!,6!/9!

$$\frac { 15 ! } { 12 ! } , \frac { 6 ! } { 9 ! }$$

Sort

$$\frac{1}{504},2730$$

Solution Steps

The factorial of 15 is 1307674368000.

$$sort(\frac{1307674368000}{12!},\frac{6!}{9!})$$

The factorial of 12 is 479001600.

$$sort(\frac{1307674368000}{479001600},\frac{6!}{9!})$$

Divide 1307674368000 by 479001600 to get 2730.

$$sort(2730,\frac{6!}{9!})$$

The factorial of 6 is 720.

$$sort(2730,\frac{720}{9!})$$

The factorial of 9 is 362880.

$$sort(2730,\frac{720}{362880})$$

Reduce the fraction \frac{720}{362880} to lowest terms by extracting and canceling out 720.

$$sort(2730,\frac{1}{504})$$

Convert decimal numbers in the list 2730,\frac{1}{504} to fractions.

$$2730,\frac{1}{504}$$

To sort the list, start from a single element 2730.

$$2730$$

Insert \frac{1}{504} to the appropriate location in the new list.

$$\frac{1}{504},2730$$

Evaluate

$$2730,\frac{1}{504}$$