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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] New post 12 Dec 2007, 11:15
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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!
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 [#permalink] New post 12 Dec 2007, 12:21
Difficult one

M E D I T R A N
E R A N
E

E _ _ R
M 7
E 8
D 7
I 7
T 7
R 7
A 8
N 8

So 5x7 + 3x8=35+24=59

Cannot figure out anything other than brute force.
Tried 11C2 which made logic to me, but got 11C2=55

Do you have the answer?
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 [#permalink] New post 12 Dec 2007, 20:19
My way:

Available letters:

M E D I T R A N (8 letters)

E _ _ R

We have 1 combination for E and 1 combination for R, and also we have 8 combinations for the 2nd letter and 7 combinations for the last letter, so:

E 8 7 R = 1 * 8 * 7 * 1 = 56
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Re: PS permutations [#permalink] New post 13 Dec 2007, 01:28
can somebody explain how to solve this one? would appreciate
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Re: PS permutations [#permalink] New post 13 Dec 2007, 02:41
young_gun 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!



Please, could you explain that to me so that I can easily understand?? I am very bad at perms!
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Re: PS permutations [#permalink] New post 13 Dec 2007, 03:23
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marcodonzelli wrote:
Please, could you explain that to me so that I can easily understand?? I am very bad at perms!


we should complete word E _ _ R using set {M-1, E-2 (one E we use as the first letter), D-1, I-1,T-1,R-1 (one R we use as the last letter) ,A-2,N-2}

So, the set consist of 5 single letters and 3 pairs of letters.

1. for second position we have 8 cases (or 5+3)

2. for third position we have either 8 cases (second letter is from a pair) or 7 cases (second letter is single letter).

Therefore,
N=(3*8+5*7)=59
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Re: PS permutations [#permalink] New post 13 Dec 2007, 04:17
Please, could you explain that to me so that I can easily understand?? I am very bad at perms![/quote]

we should complete word E _ _ R using set {M-1, E-2 (one E we use as the first letter), D-1, I-1,T-1,R-1 (one R we use as the last letter) ,A-2,N-2}

So, the set consist of 5 single letters and 3 pairs of letters.

1. for second position we have 8 cases (or 5+3)

2. for third position we have either 8 cases (second letter is from a pair) or 7 cases (second letter is single letter).

Therefore,
N=(3*8+5*7)=59

I understand point 1 and point 2 as well...but why N=(3*8+5*7)?thanks
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Re: PS permutations [#permalink] New post 13 Dec 2007, 04:37
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marcodonzelli wrote:
I understand point 1 and point 2 as well...but why N=(3*8+5*7)?thanks


for letters of E,A,N at second position we have 8 cases for third one. So, 3*8
for letters of M,D,I,T,R at second position we have 7 cases for third one (we cannot use, for example, M twice). So, 5*7
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Re: PS permutations [#permalink] New post 13 Dec 2007, 13:32
young_gun 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!


We have 11 letters after E and R occupied their places. But E, A and N show up twice each. So we have 8 distinct letters for 2 places.
For the second place - 8 letters
for the third - 7 letters
Number of variants - 8*7=56, but we have to take into account additional 3 variants with double letters EAAR, ENNR, EEER.
So the ultimate calculation is 56+3=59
Re: PS permutations   [#permalink] 13 Dec 2007, 13:32
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