My recommendation on this problem is to simply list them. If you want to think about it in terms of Slots or Anagrams, you can read below, but it's really more complicated than it needs to be. The basic issue with the Slots and Anagrams approaches is that we need to subtract out the duplicate issues. Really, using these techniques are more applicable and helpful when we have more complex problems.

Hope that helps.



Slots Approach
If we use the slots approach, we know we need to select two slices of bread. For each slice, we have two choices: either wheat or rye. So we have (2)(2) = 4.

However, in this calculation, note that we're actually listing FOUR possibilities: WW, WR, RW, and RR. If it doesn't matter which is the bottom or top slice, we have a duplicate: WR is the same as RW. So we have to subtract it out. 4 - 1 = 3.

Anagram Approach
The Anagram Approach requires us to list out all four breads. Then we'll put a "Y" if we select it, and a "N" if we do not.

W1 W2 R1 R2
Y, Y, N, N

If we want to determine how many ways to arrange YYNN, it is 4!/(2!2!) = 6. If we list this out, we find that we have FOUR duplicates:
W1R1, W1R2, W2R1, W2R2 are all the same combination; three of them are extra. So 6 - 3 = 3.

_________________
Ben Ku
Instructor
ManhattanGMAT

As Ben said, simple logic will solve this problem much quicker and without confusion than the two methods.

Just imagine you have two types of breads and how many different combinations can be possible for making a sandwiches

Wheat and Wheat, Wheat and Rye, Rye and Rye.

Exactly.

_________________
Ben Ku
Instructor
ManhattanGMAT