A string of odd and even numbers to group in three sets using combinatorics?

Question

I need help with combinatorics problem. The task is this: There are 9 numbers which are: 1,3,5,2,4,6,8,10,12. I need to group these numbers in 3 sets with 3 elements in every set, but there is one condition, the sum of the elements in every group needs to be odd.

I don't know what should i use, i think permutation but i don't know how to set up the answer!

Thanks very much!

Answer 1

Note that there are three odd numbers, so each group must have exactly one odd number, or else some group would have only even numbers and therefore have an even sum. We now need to assign two even numbers to each odd number, and this can be done by ordering six even numbers in any order, and splitting them into three groups of two, then dividing by $8$ since the order in the set does not matter. So we obtain $\frac{6!}{2^3}$ possible groupings.