# Video: A Difficult Combinatorics Problem from the New Official Guide!

The 2016 Official Guide is not a major difference from the 11th, 12th, or 2015 editions.

This is particularly true when it comes to difficult questions. However, certain things are noticeable over time.

One of these trends has been in Combinatorics (you might think of this as Permutations and Combinations, but Combinatorics is a better umbrella term as it includes all forms of counting problems.

Sometimes GMAT Combinatorics problems involve counting problems that are embedded within Probability questions, and sometimes they are as simple as applying the Combination formula.

Arguably, trying to blindly apply any formula with a Combinatorics problem is risky. It’s a lot better to build an equation based on the description of the question implies.

This video will teach you an example of doing just that.

This is a NEW question in the Official Guide for GMAT Review 2016 (OG2016 or OG 2016), Problem Solving PS 152!

“A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?

(A) 144 (B) 152 (C) 160 (D) 168 (E) 176”

This question has an unusual structure, and can only be built from scratch.

No number of permutations or combinations equations will get you to identify the split here. Watch the video and enjoy!

Check out more at www.youtube.com/gmatcoach.

For another non-equation-based Combinatorics video, check this out:

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PS How do you prefer to work through counting problems?

PPS What is your favorite counting technique?