GMAT Quant Practice | Permutation Q2

This GMAT quant practice question is a counting methods problem solving question. The concept tested in this question is to find the number of ways a few letters from a word can be selected and rearranged such that the rearrangement adheres to a specified constraint.

Question 2: How many different four letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R?

1. 59
2. \\frac{11!}{2!×2!×2!})
3. 56
4. 23
5. \\frac{11!}{3!×2!×2!×2!})

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Video Explanation

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Explanatory Answer | GMAT Combinatorics | Reordering Q2

Step 1 of solving this GMAT Permutation Question: Select 2 letters and rearrange them

MEDITERRANEAN is a 13-letter word.
We have to form a 4-letter words that start with 'E' and ends with 'R'.
Therefore, in addition to E and R, we have to find two more letters from the remaining 11 letters.

In these 11 letters, there are 2 Ns, 2Es, and 2As and one each of the remaining 5 letters viz., M, D, I, T, and R.

Step 2 of solving this GMAT Permutation Question: List down the different posssibilities

Of the 11 letters, there are 2 Ns, 2Es, and 2As and one each of the remaining 5 letters.
The second and third positions can either have two different letters or can both be the same letters.

Case 1: When the two letters are different
We have to choose two different letters from the 8 available different choices.
This can be done in 8 × 7 = 56 ways.

Case 2: When the two letters are same
There are 3 options - the two letters can be Ns or Es or As. Therefore, 3 ways.
Total number of posssibilities = 56 + 3 = 59

Choice A is the correct answer.