Question

1. 3 students are running for a class president in a class of 70 students. How many different vote counts are possible if some student(s) do not vote.

2. In how many ways can we distribute 7 pieces of identical taffy and 8 pieces of identical licorice to 5 kids such that each kid recieves exactly 3 pieces of candy.

1. I am completely stuck. I have thought of using the "hockey stick identity", but I do not fully understand how. Thanks!
2. I tried listing out all of the possible cases, but there were way too much.

Answer 1

Q1: no idea

Q2: 2 kids get 2 pieces of taffy and 1 piece of licorice and the other three get 2 pieces of licorice and 1 piece of taffy.

Explanation:

question 2 is quite obvious but no one can get the same amount of everything so the answer that i gave makes the most sense.