In S_3, an even permutation must have an odd number of orbits. True or False? Well, somehow i considered the unit cycle of S_3 : (123). And since it can be expressed as a product of 2 transpositions mainly: (12)(13) which i believe proved S_3 to be an even permutation. I have a feeling that the statement is true...
However, i'm not too sure because can't seem to understand the second part of the statement: "...must have an odd number of orbits". 
Any help would do.

Hint: The orbit-stabilizer theorem could be of use.  Choose any even permutation $s \in S_3$.
$$|G_s||O_s| = |S_3| = 6$$
Where $G_s$ is the subgroup of elements that fix $s$ (the stabilizer) and $O_s$ is the set of elements in the orbit of $s$.  Now try to find the order of the stabilizer subgroup, noting that an even permutation composed with an even permutation is even, and an even permutation composed with an odd permutation is odd.
