Unsolved Problems (to me, at least)  you have 5 identical dimes, 6 identical quarters, and 10 identical pennies. How many different groups of 5 coins can you make? Swapping out a dime for another dime wouldn't change the group, and the order in which they are selected doesn't matter. I'm most interested in an algorithm that would solve a more complex version of this problem  just an organized list of possibilities isn't an ideal solution. This is analogous to the distinguishable permutation problem, for which there is a simple formula; here, however, order doesn't matter: this is a distinguishable combinations problem.
 You've entered a lottery in which there are 35 winners chosen. There are 619 total entrants, with varying numbers of tickets from 1 up to 64. There are 1801 total tickets. You have 2 tickets; what is the probability that you get selected? (I think that this depends on the specific arrangement of tickets distributed  ask me if you want those data, or consider just starting with a smaller analogous problem; this is the way in which entrants were chosen for the 2013 Hardrock 100 ultramarathon).
