please explain step by step

4. (30 pts) You may express your answers to the following questions using factorials, expo- nents, and binomial coefficients. (a) Suppose you have 100 dimes to distribute into 3 bins marked "$ for chocolate", "$ for broccoli", and "$ for savings". In how many ways can the dimes be distributed if each bin ends up with at least 5 dimes? (b) Let S = {1, 5, 10, 25, 50}. Suppose subsets are randomly selected from P(S), the power set of S. How many subsets must be selected to guarantee that there are at least two subsets of cardinality 3? (c) Suppose you have a large number of dimes and nickels. Write a generating function that can be used to find the number of ways to make $10.00 in change combining any number of dimes and no more than 50 nickels. Which term of the function will corre- spond to the