We have to distribute m distinguishable toys, k identical candy bars to 12 children in the following ways: a. How many ways can we distribute toys if each child can get any number of toys? b. How many ways can we distribute candy if each child can get any number of candy bars? c. How many ways can we distribute the (identical) candy bars if each child can get at most 1 and k<12 d. How many ways can we distribute (distinct) toys if each child can get at most 1 and m>12 (extra toys are saved for next year) e. If m=15 and k=9 how many ways can we distribute the objects if each child gets exactly 2 goodies. Parts a and b I feel confident about (I got 12^m for part a and C(k+11, k) for part b). Part c I tried doing by cases, such as 11 children can have 0 or 1, then 10 children can have 0 or 1 etc. So I figured it would be 2^11 Parts d and e I truly feel lost on and have scoured the internet for different methods and haven't felt confident about anything I've read! Thank you for any starting hints or tips.