Question: Number of Routes

Comment on Number of Routes

I always found this question difficult but with your explanation it's easy. Thank you so much, Brent.
greenlight-admin's picture


Hello Brent,
Wonderful explanation and techniques for counting questions. My question is, why there is no use of Permutation formula in your explanations? What I have learnt before is, when there is order for counting, use permutation and when there is no order for counting, use Combination. Now using this logic and the respective formulas, though I was not able to solve all the difficult questions correctly, but I was still able to recognize a pattern whether the question is of permutation or combination. But here even when the logic of solving and your explanations are so good and relevant, I'm still not able to recognize a pattern as to which method to use for which type of question, or to understand whether this is a restrictive method question, whether we have to use Fundamental Counting principle or whether we have to use the MISSISSIPPI rule. I'm little bit confused with this. Can you provide a brief summary on the type of questions in Counting method and what method to use for which type of questions? Just a rough idea. I do not want to mug up, but I want the method to solve questions when I see a question. I kind of get stuck up thinking how to proceed. This was not the case in other modules. Please help.
greenlight-admin's picture

I'm not a big fan of permutations. I say this because many students are under the impression that all counting questions are either combination questions or permutation questions.

The truth is that there are very few GRE permutation questions, and those questions can be solved using the Fundamental Counting Principle (FCP).

In fact, the FCP can be used to solve the majority of counting questions you'll encounter.

More on this topic here:

Your question is tough one to answer. However, we do have a video that describes the steps you can use to determine HOW which strategy apply for a given question.

Yes, my bad. Actually, I did not complete the full module and asked you the doubt which I had. As you said, yes, the FCP and other counting techniques indeed help a lot and make much sense to solve counting question than permutations. Thanks again for your beautiful strategies and technique. Really helpful.

This is an amazing strategy !!!
greenlight-admin's picture

Glad you like it!

It is just so easy to miss out on the tiny details in the question.

I didn't read the question properly and didn't read "only right or down", the question then became so difficult to solve.

Sometimes I feel that the answer to a question lies in the tiniest of its details.
greenlight-admin's picture

You're absolutely right; one word can totally change the question!


Very clever solution.

Wow, I answered this one correctly in less than a minute! I'm loving these math videos a lot. After reading through the ETS Official Guides, EmpowerGRE online modules, and Manhattan Prep, I'm seeing different techniques here that work wonderfully. Just when you think you've exhausted all prep materials and can't possibly see something different, greenlight shows you the light!
greenlight-admin's picture

A new tagline: Greenlight shows you the light!
I love it!!

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