The GMAT Sample Math question is a combinatorics problem solving question. The concept tested in this question is to find the number of ways the letters of word can be rearranged.
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?
A. 59
B.
C. 56
D. 23
E.
The correct choice is (A) and the correct answer is
59
The first letter is E and the last one is R.
Therefore, one has 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 have both the letters to be the same.
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 three can be either Ns or Es or As. Therefore, 3 ways.
Total number of posssibilities = 56 + 3 = 59
eBooks on Permutation Combination & Probability
This ebook with about 100 pages covers all major concepts in Permutation combination (combinatorics) and Probability. Includes typical GMAT like problems such as "tossing of coins", "rolling of dice" and "selecting cards from a pack of cards" 
This eBook is a practice test comprising 95 questions on Permutation, Combination and Probability. These questions are objective type multiple choice questions. Each question is provided with correct answers and detailed explanations at the end of the test. 
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