A. You have 5 identical apples that you want to give to friends, and you have 5 friends who would like apples. Their names are Amy, Bert, Carl, Dina, and Eric. You don’t have to be fair and give the same number of apples to every friend, but you do need to give whole apples (can’t split them). In how many ways can you do this?
B. What if instead of 5 unique friends, you have 5 identical boxes to store the apples so that it doesn’t matter which one gets more (ie, 1 apple in the first box and 2 apples in the second box is the same as 2 apples in the first box and 1 apple in the second box)?
C. What if you have 5 uniquely different apples to give to 5 uniquely different friends?
D. What if you have 10 identical apples and 10 different friends?
E. What if you have n identical apples and n friends?