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The number of arrangement of letters of the word BANANA in

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The number of arrangement of letters of the word BANANA in [#permalink] New post 28 Oct 2013, 04:26
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Difficulty:

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Question Stats:

54% (01:57) correct 46% (01:07) wrong based on 67 sessions
The number of arrangement of letters of the word BANANA in which the two N's do not appear adjacently is:

A. 40
B. 50
C. 60
D. 80
E. 100
[Reveal] Spoiler: OA
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Re: The number of arrangement of letters of the word BANANA in [#permalink] New post 28 Oct 2013, 06:03
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saurabhprashar wrote:
The number of arrangement of letters of the word BANANA in which the two N's do not appear adjacently is:

A. 40
B. 50
C. 60
D. 80
E. 100


Total # of arrangements of BANANA is 6!/(3!2!) = 60 (arrangement of 6 letters {B}, {A}, {N}, {A}, {N}, {A}, where 3 A's and 2 N's are identical).

The # of arrangements in which the two N's ARE together is 5!/3!=20 (arrangement of 5 units letters {B}, {A}, {A}, {A}, {NN}, where 3 A's are identical)..

The # of arrangements in which the two N's do not appear adjacently is {total} - {restriction} = 60 - 20 = 40.

Answer: A.
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Re: The number of arrangement of letters of the word BANANA in   [#permalink] 28 Oct 2013, 06:03
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