we have 4 distinct ice cream flavors to choose from
How many different combinations of flavors of three scoops of ice cream are possible if it is permissible to make all three scoops the same flavor ?
The answer is
all diff + all similar + 2 similar and 3rd diff
4 choose 3 + 4 choose 1 + 4P2 (the last one is the permutation)
Can any one justify 4P2 ?