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Intern Joined: 14 Dec 2011 Posts: 13 Location: India Concentration: Technology, Nonprofit GMAT 1: 640 Q48 V29 GMAT 2: 660 Q45 V35 GPA: 3.5 WE:Information Technology (Computer Software) The number of arrangement of letters of the word BANANA in
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Hide Show timer StatisticsThe number of arrangement of letters of the word BANANA in which the two N's do not appear adjacently is: A. 40 Math Expert Joined: 02 Sep 2009 Posts: 86775 Re: The number of arrangement of letters of the word BANANA in
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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 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. Senior Manager Joined: 15 Feb 2018 Posts: 453 The number of arrangement of letters of the word BANANA in
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Bunuel GMAT Club Legend Joined: 11 Sep 2015 Posts: 6802 Location: Canada
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philipssonicare wrote: Bunuel I call these questions MISSISSIPPI questions. Cheers, Brent Hanneson – Creator of gmatprepnow.com GMAT Club Legend Joined: 11 Sep 2015 Posts: 6802 Location: Canada
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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 ---------ASIDE------------- If there are n objects where A of them are alike, another B of them are alike, another C of them are alike, and so on, then the total number of possible arrangements = n!/[(A!)(B!)(C!)....] So, for example, we can calculate the number of arrangements of the letters in MISSISSIPPI as follows: In BANANA, there are: IMPORTANT: Among these 60 outcomes, there are some outcomes
that break the rule about N's not appearing next to each other. First "glue" the 2 N's together, to get one "super letter" NN Number of arrangements that adhere to the rule = 60 - 20 = 40 Answer: A Cheers, Brent Hanneson – Creator of gmatprepnow.com Intern Joined: 25 May 2014 Posts: 3 Re: The number of arrangement of letters of the word BANANA in [#permalink]
Hi Bunuel, Intern Joined: 25 May 2014 Posts: 3 Re: The number of arrangement of letters of the word BANANA in
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Hi Bunuel GMAT Club Legend Joined: 18 Aug 2017 Status:You learn more from failure than from success. Posts: 7207 Location: India Concentration: Sustainability, Marketing GPA: 4 WE:Marketing (Energy and Utilities) Re: The number of arrangement of letters of the word BANANA in [#permalink]
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 BANANA = Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 11847 GPA: 3.82 Re: The number of arrangement of letters of the word BANANA in [#permalink]
Total number of ways to arrange the letters of the given word BANANA : \(\frac{(6!) }{ (3! * 2!)}\) = 60 Number of ways if both NN are adjacent: Consider 'NN' as 1 letter: BAAA (NN) => We have 5 letters to arrange, therefore: 5!. => Both 'NN' can be arranged it 2! ways. As we have repetition (3A's and 2N's) therefore: => \(\frac{(5!) *(2!) }{ (3! * 2!)}\) = 20 The number of ways 'NN' won't be adjacent to each other: 60 - 20 = 40. Answer A Manager Joined: 26 Jul 2020 Posts: 219
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YassiHASHMI wrote: Hi
Bunuel We don't consider N2N1 as a different arrangement since the two letters "N" are identical. There is no difference in the arrangement if you swap the positions of N. Hope it is clear. VP Joined: 11 Aug 2020 Posts: 1409 Re: The number of arrangement of letters of the word BANANA in
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6! / 3! x 2! = 60 <--- Total # of permutations with repeats 60 - 20 = 40 <--- Ps where they are not together Answer is A. "Do not pray for an easy life, pray for the strength to endure a difficult one." - Bruce Lee Manager Joined: 09 Aug 2022 Posts: 75 Location: India Concentration: General Management, Leadership GPA: 4 WE:Design (Real Estate) Re: The number of arrangement of letters of the word BANANA in [#permalink]
arrangement = 6!/2!*3!= 60 ways Posted from my mobile device Re: The number of arrangement of letters of the word BANANA in [#permalink] 15 Aug 2022, 08:19 Moderators: Senior Moderator - Masters Forum 3085 posts How many arrangements are there of the letters BANANA such that no two n's appear in adjacent positions?Hence number of way in which two N′s do not appear adjacently =60−20=40.
How many ways can the letters of BANANA be arranged?So 60 distinguishable permutation of the letters in BANANA.
How many permutations of the letters of the word BANANA are possible?m! In the word BANANA, we have six letters. The total number of permutations of 6 letters = 6!
How many arrangements are there of the letters in BANANA such that the letter B is followed by an A '?The answer is 46,080.
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