# GMAT Math Practice: Rearranging Letters

Concept: Selecting objects from a set. Reordering with a constraint.

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 some letters from a word can be selected and rearranged with a constraint.

#### Question: 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. $\frac{11!}{3!*2!*2!*2!}\\$

#### Select 2 letters and rearrange them

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

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 have both as same letters.

##### Case 1: When the two letters are different

One has 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.

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