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# How many different four letter words can be formed (the

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How many different four letter words can be formed (the [#permalink]

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20 Sep 2005, 23:40
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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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21 Sep 2005, 04:11
I'd go for B

you have 13 letters, two of them are alreadty used, so you have 11! possibilities.

There are two As Ns and Es so you have to divide by 2!*2!*2!

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21 Sep 2005, 09:35
I came up with C as an answe. Explaination as follows

1) Ignoring repetitions in all there 8 letters in total.
2) First and last letters are E & R
3) We need to find number of ways middle 2 letter combination can be generated.

As it is not mentioned that E & R can not appear in these two letters I calculated 8P2 (permutation) for an answer.

Please let me know if I am wrong.
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21 Sep 2005, 10:05
MBAHopeful wrote:
I came up with C as an answe. Explaination as follows

1) Ignoring repetitions in all there 8 letters in total.
2) First and last letters are E & R
3) We need to find number of ways middle 2 letter combination can be generated.

As it is not mentioned that E & R can not appear in these two letters I calculated 8P2 (permutation) for an answer.

Please let me know if I am wrong.

why are you taking 8 letters only. Isnt 11 letters left to be chosen to fit 2 middle numbers?

the numbers left for middle spots:
E- 2
A - 2
N - 2
R - 1
4 - single occurance letters

we need to find all distinct 2 letter combinations among them. Not sure how to calculated it. Initially i thought it would be:
11p2/2! * 2! * 2!

but calculation results in fraction.

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21 Sep 2005, 11:26
duttsit wrote:
MBAHopeful wrote:
I came up with C as an answe. Explaination as follows

1) Ignoring repetitions in all there 8 letters in total.
2) First and last letters are E & R
3) We need to find number of ways middle 2 letter combination can be generated.

As it is not mentioned that E & R can not appear in these two letters I calculated 8P2 (permutation) for an answer.

Please let me know if I am wrong.

why are you taking 8 letters only. Isnt 11 letters left to be chosen to fit 2 middle numbers?

the numbers left for middle spots:
E- 2
A - 2
N - 2
R - 1
4 - single occurance letters

we need to find all distinct 2 letter combinations among them. Not sure how to calculated it. Initially i thought it would be:
11p2/2! * 2! * 2!

but calculation results in fraction.

I thought we need to ignore multiple occurrences of the same letter in the word and hence I came up with number 8. Let me know if my thinking is wrong.
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21 Sep 2005, 13:08
I get 59

one E and R are fixed besides that there are 11 letters for two places out of that 8 are distinct so they can be used to produce

8*7 = 56 combinations

plus three letters are repeated twice so they can make 3 more words..

so the answer is 56+3 = 59
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23 Sep 2005, 01:09
I agree with ranga41, I read the question wrong and thought they were asking for 8 letter words.

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02 Jan 2006, 11:44
I got 59 too. Except I used a different approact.

We have 3 letter with 2 occurence and 5 with single. To pick 2 letters, I can do it in two different ways.

1. pick 3 repeated then any 8.
2. pick 5 single and then any 7.

result 3*8 + 5*7 = 59.

- Vipin

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22 Jan 2006, 10:53
ranga41 wrote:
I get 59

one E and R are fixed besides that there are 11 letters for two places out of that 8 are distinct so they can be used to produce

8*7 = 56 combinations

plus three letters are repeated twice so they can make 3 more words..

so the answer is 56+3 = 59

The word formed by two 'different E's' will read the same and should be considered as a same word.

Also,

out of 13, 2 are used up E and R

you are left with 11 alphabets with two N's, 2 A's and 2 E's to be filled in 2 places

should it not be

11x10 -3 = 107
words

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22 Jan 2006, 13:02
old_dream,

Obviously I too didn't get this right the first time.

But here is what I think:

MEDITERRANEAN has

13 letters with
3 - E's
2 - R's
2 - N's
2 - A's

The words to be formed are of the type E _, _, R

Consider all the single characters withour repititions i.e, we need to choose from : (M, D, I, T, R) + 1 from each of (E, N, A) = 8 characters.

So No of words = 8*7 = 56

Now we had excluded the possibility of (2 Es, 2Ns, 2A's)

So we have only 3 more words to consider:
EAAR
ENNR
EEER

Hence 56+3 = 59
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22 Jan 2006, 13:02
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# How many different four letter words can be formed (the

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