The Math Division

I

Somewhat challenging combinatorics problem:

Five ping pong balls are placed in an urn. They are numbered one to five. Without looking, Kathy selects some number of balls (at least one) from the urn. If the numbers on the balls selected are added together, how many selections will result in an odd sum? (count in such a way that order doesn’t matter, i.e., 1-4 is the same as 4-1).

https://www.instagram.com/p/CFQBYhDpswx/?igshid=1xdpcg29cxgh0

Oblate Spheroid in Geogebra.