Question 48934
Look at the solution by Longjonsilver. 
His solution shows that there are 720 combinations but he has assumed that the three odd numbers go first then the two even numbers.
There are 10 different ways in which the 3 odd and 2 even numbers can be distributed.
O	O	O	E	E
O	O	E	E	O
O	O	E	O	E
O	E	O	E	O
O	E	O	O	E
O	E	E	O	O
E	O	O	E	O
E	O	O	O	E
E	O	E	O	O
E	E	O	O	O
This brings the total number of solutions to 720 * 10 = 7200 which meet the original conditions.