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# How many different four letter words can be formed (the words need not

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Posts: 24
How many different four letter words can be formed (the words need not  [#permalink]

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19 Jan 2019, 18:55
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Question Stats:

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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!)

I came across this question and this was how I had solved it.

MEDITTERRANEAN

E.....A

Fix positions E and A. So out of the available 'E's, choose 1 , 3C1

then Out of the available 'R's , chose 1 , 2C1

Remaining characters = 12 (out of which there are 2As , 2Es, 2Ts, 2Ns)

Now we need to choose 2 out of 12 (with 4 identical sets)

3 no. of different ways to arrange 4 letter words = 12C2/(2!2!2!2!) x 3 x 2

Could you help me understand where I went wrong?
Retired Moderator
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 989
Location: India
GPA: 3.64
Re: How many different four letter words can be formed (the words need not  [#permalink]

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19 Jan 2019, 20:56
Leonaann wrote:
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!)

I came across this question and this was how I had solved it.

MEDITTERRANEAN

E.....A

Fix positions E and A. So out of the available 'E's, choose 1 , 3C1

then Out of the available 'R's , chose 1 , 2C1

Remaining characters = 12 (out of which there are 2As , 2Es, 2Ts, 2Ns)

Now we need to choose 2 out of 12 (with 4 identical sets)

3 no. of different ways to arrange 4 letter words = 12C2/(2!2!2!2!) x 3 x 2

Could you help me understand where I went wrong?

Hi Leonaann
Please refer to the below post:
https://gmatclub.com/forum/how-many-dif ... 57055.html
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Re: How many different four letter words can be formed (the words need not   [#permalink] 19 Jan 2019, 20:56
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# How many different four letter words can be formed (the words need not

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