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In how many different ways can the letters A, A, B

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Re: Permutation Problem [#permalink] New post 26 May 2013, 23:08
Expert's post
cumulonimbus wrote:
Bunuel wrote:
tania wrote:
In how many different ways can the letters A,A,B,B,B,C,D,E be arranged if the letter C must be to the right of the letter D?
A.1680
B.2160
C.2520
D.3240
E.3360

Can someone explain how I should approach to solve the above problem?


We have 8 letters out of which A appears twice and B appears three time. Total number of permutation of these letters (without restriction) would be: \frac{8!}{2!3!}=3360.

Now, in half of these cases D will be to the right of C and in half of these cases to the left, hence the final answer would be \frac{3360}{2}=1680

Answer: A.


Hi Bunnel,

If the question were:

Cases in which A is to the right of C?
tot=8!/2!*3!=3360

A to right of C = 3360/(2!)^2?


Both A's or just one A? Anyway, in this case the problem will be out of the scope of the GMAT, so I wouldn't worry about it.

Questions about the same concept to practice:
susan-john-daisy-tim-matt-and-kim-need-to-be-seated-in-130743.html
meg-and-bob-are-among-the-5-participants-in-a-cycling-race-58095.html
six-mobsters-have-arrived-at-the-theater-for-the-premiere-of-the-126151.html
mary-and-joe-are-to-throw-three-dice-each-the-score-is-the-126407.html
goldenrod-and-no-hope-are-in-a-horse-race-with-6-contestants-82214.html

Hope it helps.
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Re: In how many different ways can the letters A, A, B [#permalink] New post 26 Jul 2014, 20:08
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Re: In how many different ways can the letters A, A, B   [#permalink] 26 Jul 2014, 20:08
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