Latest GMAT Aptitude Question SOLUTION: 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 let

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(#M40010429) GMAT Numerical Ability question Keep an EYE

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. 11!/2!*2!*2!

C. 56

D. 23

E. 11!/2!*2!*2!*3!

Asked In GMAT Gourav Rusiya (11 years ago)

Unsolved Read Solution (6)

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Read Solution (6) :

PARAG KAMRA  (11 years ago)

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 possibilities = 56 + 3 = 59

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siri  (11 years ago)

solution:A)59
MEDITERRANEAN (13 LETTERS) - ER( 2 letters)= 11 letters
case1)considering blank spaces to be filled by repeated letters( NN,AA,EE)there will be 3 ways.(11-3=8 remaining letters)
case2) considering non repeated letters can be arranged in 8P2 ways.
hence total arrangements= 8p2+3= 56+3=59

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aanchal sharma  (11 years ago)

option E is the correct answer.because total number of words in MEDITERRANEAN are 13,now E and R are fixed at first and last position...remaining words are 11.which can be arranged in 11! ways..
11!/2!*2!*2!*3!

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santhi   (9 years ago)

59 ways.
e_ _r
3 ways(aa,nn,ee) remaining letter=8
8c1*7c1=56
56+3=59

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Richa Mehra   (6 years ago)

for all those with ans 59 guys if u carefully observe there are 3 E ,2R, 2N, 2A in the letter MEDITERRANEAN so all possible ways such that start with E and end with R =
11!/2!2!2!3!

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Sivaprasanthi  (11 years ago)

Given that E and R is fixed at first & last position, therefore remaining 11!/(3!*2!*2!*2!). Repetiton:3!-E, 2!-R,2!-A,2!-N.

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