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Current Student
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How many different four letter words can be formed (the [#permalink]
 12 Dec 2007, 12:15
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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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Manager
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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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Manager
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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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Manager
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Re: PS permutations [#permalink]
13 Dec 2007, 02:28
can somebody explain how to solve this one? would appreciate
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VP
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Re: PS permutations [#permalink]
13 Dec 2007, 03:41
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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CEO
Joined: 17 Nov 2007
Posts: 3608
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
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Re: PS permutations [#permalink]
13 Dec 2007, 04:23
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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VP
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Re: PS permutations [#permalink]
13 Dec 2007, 05:17
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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CEO
Joined: 17 Nov 2007
Posts: 3608
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
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Re: PS permutations [#permalink]
13 Dec 2007, 05:37
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]
13 Dec 2007, 14:32
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
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Re: PS permutations
[#permalink]
13 Dec 2007, 14:32
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