Probability problem - how did Princeton Review solve this?

[maxim730]

I can't figure out how Princeton Review solved the below problem, their explanation doesn't make sense to me.

If anyone can break it down, that would be great!!

Q:

Ten strips of paper are numbered 1 to 10 and placed in a bag. If three numbers are drawn from the bag at random, what is the probability that the sum of the numbers drawn will be odd?

A) 1/12
B) 5/36
C) 15/36
D) 1/2
E) 11/18

OA is D

Princeton explanation (This is an image I added, I didn't want to type it out_):

https://img143.imageshack.us/my.php?image=problemzn4.jpg

[maxim730]

That makes sense, thanks Mark!

[thankont]

Mark can we just simply say that since there are same number of odd and even numbers from 1 - 10 (5 each), and since odd number can be formed the same number of ways as an even number then right away p=1/2 ?