How many 3-letter codes can be formed by choosing GMAT

How many 3-letter codes can be formed by choosing, without replacement, 3 letters from the word PEPPER?

A) 6

B) 18

C) 19

D) 27

E) 30

Yet again we’re faced with a GMAT combinatorics question that doesn’t have anything to do with true permutations or combinations. That means you won’t be able to apply a formula. 

Remember, the GMAT isn’t testing you on whether you know how to plug and chug, so expect questions like these where you have to use your brain rather than some bullshit Excel macro to solve.

So what steps do we need to take to figure this out? 

As a first step, you might consider applying Mississippi Rule to figure out the total number of ways that the letters in PEPPER can be organized. Unfortunately, however, that won’t actually be helpful because you’re actually limited to three letters.

So actually we need to ask this:

1. Which three letters do we choose from the word PEPPER?

This then depends on whether the letters can be repeated or not. Therefore, we need to consider situations with no repeats, two repeated letters, and three unique letters. 

2. How many of each type do we have?

No repeats: this is only possible in the case PPP, so there’s only 1. 

Two repeated letters: this is possible for PPE, PPR, EEP, and EER. Each of these has possibilities by Mississippi Rule. Or given that they’re easy to count out, you’re welcome to hand-count these this way, where it’s quite obvious that each one reflects three possibilities…

PPE

PEP

EPP

etc…

There are four groups, each of which has three variations, for a total of 12 possibilities here.

Three unique letters: our only possibility for the three letters is PER, of course, but remember that the order among these letters must be considered as well. 

Given that we have three unique options, the total number of possibilities will be .

All we need to do now is sum these values to find the total number of possibilities for 3-letter codes:

No repeats: 1

Two repeated letters: 12

Three unique letters: 6

Sum: 19 

Therefore, we find that there are 19 different possible 3-letter codes that can be created from the letters of the word PEPPER. 

Like what you see here? There’s even more of this shit available in The Permutations and Combinations Guide.

Now’s the time to write a bit more garbage so that the Death Star thinks I’m not talking shite, so that’s why I’ll say how many 3-letter codes one more time.