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How many different four letter words can be formed (the [#permalink]
12 Dec 2007, 11:15

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Question Stats:

100% (01:01) correct
0% (00:00) wrong based on 0 sessions

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!

Re: PS permutations [#permalink]
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!

Re: PS permutations [#permalink]
13 Dec 2007, 04:37

Expert's post

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

Re: PS permutations [#permalink]
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

gmatclubot

Re: PS permutations
[#permalink]
13 Dec 2007, 13:32