I have 3 pieces of candy to place in 4 lunch boxes. In how many ways can I do this if Exactly two of the candies are the same (but the third is different) and all of the lunch boxes are different?
+128407 We can place all three candies in any box = 4 ways
We can place the same candies in any one of the 4 boxes and the different one in any of the remaining 3 boxes
= 4 * 3 = 12 ways
We can place the different candy and either piece of the same candy in any of the 4 boxes and the other piece of the same candy in any of the remaining 3 boxes = 4 * 3 = 12 ways
[ The same candies are indistinguishable, so choosing either doesn't matter]
We can place the different candy in one of the four boxes and choose any 2 of the remaining 3 boxes to put one piece of each of the same candies in = 4 * 3C2 = 4 * 3 = 12 ways
So......
4 + 3(12) = 40 ways
