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Permutation and Combination - December 10, 2004
The GMAT Sample Math question for the day is from the topic Permutation and Combination.
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?
A. 59
B. 
C. 56
D. 23
E. 
The correct choice is (A) and the correct answer is 59.
Explanatory Answer
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
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