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by Amrabdelnaby » Fri Nov 13, 2015 11:04 am
Could you please explain the below 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. 11! / (2!*2!*2!)

C. 56

D. 23

E. 11! / (3!*2!*2!*2!)
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Counting question

by Brent@GMATPrepNow » Fri Nov 13, 2015 1:58 pm
Amrabdelnaby wrote:Could you please explain the below 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. 11! / (2!*2!*2!)
C. 56
D. 23
E. 11! / (3!*2!*2!*2!)
Since the first and last letters are FIXED, we have E _ _ R
We need only fill in the two blanks with the remaining letters.

There are two cases to consider:
a) the two letters in the middle are the SAME
b) the two letters in the middle are the DIFFERENT

a) the two letters in the middle are the SAME
There are 3 pairs of duplicate letters: E,E, A,A and N,N
So, the words could be EEEE, EAAE and ENNE
There are 3 words in which the 2 middle letters are the SAME.

b) the two letters in the middle are the DIFFERENT
There are 8 different letters to choose from: E,A,N,M,D,I,T,R
So, we can select a letter for the first blank in 8 ways
So, we can select a letter for the second blank in 7 ways (since the 2nd letter cannot be the same as the 1st letter)
So, the TOTAL number of ways to fill in the two blanks = (8) (7) = 56
There are 56 words in which the 2 middle letters are DIFFERENT.

TOTAL number of 4-letter words = 3 + 56
= 59

Answer: A

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Mon Sep 17, 2018 5:36 am, edited 1 time in total.
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by joseph2017 » Sun Jul 03, 2016 6:05 am
Hi Brent,

The question clearly says ' How many different 4 letter words can be formed', so shouldn't the arrangement be E-(11*10)-R .

Joseph.
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by Brent@GMATPrepNow » Mon Sep 17, 2018 5:37 am
joseph2017 wrote:Hi Brent,

The question clearly says ' How many different 4 letter words can be formed', so shouldn't the arrangement be E-(11*10)-R .

Joseph.
Good catch! (someone else just alerted me to my error)
I have edited my response accordingly.

Cheers,
Brent
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