Number of ways of choosing atmost 'p' balls from a set of 'a' red balls and 'b' green balls such that red balls are chosen in odd number

Question

I am given \'n\' balls out of which \'a\' are red and \'b\' are green (a+b = n). I have to choose \'p\' or fewer balls but the set of balls that I\'ve chosen should contain an o