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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?

Jun 22, 2019

#1
0

CPhill noooooooo

Jun 22, 2019
edited by Guest  Jun 22, 2019
#2
+111329
+1

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

Jun 22, 2019
#3
+1

Thank you so much!

Jun 22, 2019