Answer Happy

For each problem, display the final numerical answer and the
equation(s) used to form the
answer. Leave combinations, permutations, factorials, and exponents
intact.

Good example:

C(6, 3) – C(5, 2) = 10

Bad examples:

10 no equation
C(6, 3) – C(5, 2) no final answer
20 – 10 = 10 did not leave combinations intact
3. (20 points, 4 points each) You have 15 marbles and three jars
labeled A, B, and C. How many
ways can you put the marbles into the jars...
a. if each marble is different?
b. if each marble is the same?
c. if each marble is the same and each jar must have at least two
marbles?
d. if each marble is the same but each jar can have at most 6
marbles?
e. if you have 10 identical red marbles and 5 identical blue
marbles?