Word Problems book, hard question set, #20

[danc]

Tommy,

Is there a way to solve this question with anagrams? I've tried it that way and can't get the right answer but it seems like there should be a way for that to work.

[tommywallach]

Hey Dan,

Hmm. I actually don't use the anagram method. Not ever. I think it's an illogical way to think about combinatorics. (I won't get into the details, but basically the anagram grid method involves including things you're not concerned about (in the numerator), then taking them out again (in the denominator). This is silly to me, so I go with the slots method.

I would have no idea how to do this with the anagram grid! (Which is another reason I don't like it: the slots method works for all questions, but the anagram grid is kinda hit or miss).

-t

[danc]

In that case is the approach used in this question applicable to all questions I would otherwise use anagrams for? In other words, using the counting principle to multiply and then subtracting the values of the constraints?

[tommywallach]

The slots method is applicable to all questions in some way. However, it is not enough on its own to do this question.

Keep in mind (and this is very important), this question is NOT realistic on the GRE. You would never get this. It's far too hard/complex for the GRE.

That being said, harder combinatorics questions (such as this one, which might appear on the GMAT) require you to simply COUNT some things, because the constraints are too complicated to include in any codified methodology (slots or anagram). This is one of those questions.

-t