In how many ways can the letters in mmmnnnppqq can be arranged with two n's together?

• MMMN(NN)PPQQ so taking two N's together we can get =9!/(3!*2!*2!) arrangements
  bow this NN can be arranged in =2!/2!=1 ways
  so total arrangements=9!/(3!*2!*2!)=15120 ways
• 8 years agoHelpfull: Yes(53) No(12)
• Ans: 7560
  since 2 n's are to be considered as one entity
  now, we have 9 letters out of which we have to select 9 and arrange them
  selecting and arranging 9= 9C9 x 9! / 3! x 2! x 2! x 2!= 7560
• 8 years agoHelpfull: Yes(23) No(15)
• count where two n's are not together=total arrangement -where the n's are together.
  total arrangement=10!/(3!*3!*2!*2!)-((8C3*3!/3!)*(7!/3!*2!*2!))=13440 ways
• 8 years agoHelpfull: Yes(9) No(2)
• 9!/(3!*2!*2!)
• 8 years agoHelpfull: Yes(6) No(2)
• i am pongadam. my solution is (9!/3!2!2!-8!/3!2!2!)
• 8 years agoHelpfull: Yes(5) No(1)
• only Krishnaveni solution is correct:10!/(3!*3!*2!*2!)-((8C3*3!/3!)*(7!/3!*2!*2!))=13440 ways
• 8 years agoHelpfull: Yes(3) No(0)
• since 2 n's are together, total number of groups available becomes 9 which can be arranged in 9! ways.
  now since, there r 3 m, 2 p and 2 q .. so it would become 9!/(3!*2!*2!).. further 2 n can be arrange themselves in 2! ways .. and being repetative total arrangemnt possible for the two grouped n is 2!/2!..
  so the answer eventually turn out to be 9!/(3!*2!*2!)
• 8 years agoHelpfull: Yes(3) No(0)
• total number of ways when two n's are together = 9!/(3!*2!*2!)
  Now subtracting the cases when three n's are together(because they are considred twice eg.= mmmn(nn)ppqq and mmm(nn)nppqq ) = 8!/(3!*2!*2!)
  therefore, total arrangements = 9!/(3!*2!*2!)- 8!/(3!*2!*2!) = 13440 ways
• 7 years agoHelpfull: Yes(3) No(0)
• 9!/(3!*2!*2!)
• 8 years agoHelpfull: Yes(2) No(5)
• in 7560 ways since in 3 N's N's is considered to b single soooooo it will bw like 9!/3!2!2!
  
• 8 years agoHelpfull: Yes(2) No(2)
• Arranging with 2 n’s together:
  Select 2 n’s out of three = 3C2 = 3
  The selected 2 n’s are considered as one.
  There will be 9 elements after combining.
  Number of arrangements,
  = [9!/(3! x 2! x 2!)] x (2!/2!) x 3
  = 11340
  In the above arrangements, some them will have 3 n’s together. We have to eliminate them.
  Number of arrangements in which 3 n’s are together, = [8!/(3! x 2! x 2!)](3!3!)
  = 420
  Number of arrangements in which 2 n’s are together,
  = 11340 – 420 = 10920
  
• 8 years agoHelpfull: Yes(2) No(0)
• total number of letters=10
  ways in which 10 letters can be arranged=10 !
  ways in which 9 letters can be arranged(since 2 n's allways occur together)-9!(arranging 9 letters)*2(since two n's can be arranged in 2! ways)
• 8 years agoHelpfull: Yes(1) No(0)
• taking 2 N's are one unit
  9!/3!2!2!1!
  
• 8 years agoHelpfull: Yes(1) No(1)
• total no.of ways in which the letters can be arranged=10!/(3!*3!*2!*2!)=25200
  taking 2 N's as 1 unit,we have to arrange MMM(NN)NPPQQ=9 letters,
  this can be done in=9!/(3!*2!*2!)=15120 ways.
  out of these 15120 ways,the 2 N's can be arranged between themselves in 2!/2!=1 way.
  thus the total no.of ways=25200-(15120*1)=10080 ways.
• 8 years agoHelpfull: Yes(1) No(0)
• 9!*2!
  9! ways for all alphabets and 2! ways for 2 ns as a unit
  
• 8 years agoHelpfull: Yes(0) No(2)
• 9!/(3!*3!*2!*2!)
• 8 years agoHelpfull: Yes(0) No(3)
• 9!*2!=725760
• 8 years agoHelpfull: Yes(0) No(0)
• mmm(nn)nppqq = 9!*2! = 725760
• 8 years agoHelpfull: Yes(0) No(0)
• Two n's together=No restriction-Three n's together
  so ans=10!/(3!*3!*2!*2!)-8!(3!*2!*2!)
• 8 years agoHelpfull: Yes(0) No(2)
• if we take 2n together then...
  mmmn(nn)ppqq=9
  so 9!/(3!*2!*2!*2!)=7560
  so 7560 is the ans.
  
• 8 years agoHelpfull: Yes(0) No(0)
• (8! * 3C2)/(3! * 2! * 2!) = 5040
• 8 years agoHelpfull: Yes(0) No(0)
• mmmnnnppqq. therefore mmmnppqq(nn).There are 9 elements in which m has 3 repeatation p has 2 q has 2 .. so 9!/(3*2*2) =362880/12= 30240. since n can be arranged in 2! ways. 30240*2! = 60480
• 8 years agoHelpfull: Yes(0) No(0)
• taking NN together we get = 9!/(3!*2!*2!)
  and NN can be arranged in = 2!
  thus total arrangements = (9!/3!*2!*2!)*2! = 30240
• 7 years agoHelpfull: Yes(0) No(0)
• 9!/(3!*3!*2!*2!)
• 7 years agoHelpfull: Yes(0) No(0)
• (NN)MMMNPPQQ (Note that NN is treated as one letter)
  Taking two N's together we can get (9!*2!)/(3!*2!*2!) arrangements ..
  (9!*2!) => NN can be arranged in 2! ways & MMMNPPQQ+(NN) = 9 letters
  (3!*2!*2!) => M is repeated 3 times, P is repeated 2 times & Q is repeated 2 times
• 6 years agoHelpfull: Yes(0) No(0)
• 13440 is correct
• 6 years agoHelpfull: Yes(0) No(0)
• ans: 7!/2! * 8!/3! 2! 2!
  
  two n's together in 7 positions -----> _m_m_m_n_p_p_q_q_ (two positions excluded)
  but two positions excluded because mmm(nn)nppqq and mmmn(nn)ppqq (three n's are together)
  and again two n's internally can be arranged in 2! ways So, 7!/2! ways two n's together and remaining letters can be arranged in 8!/3! 2! 2!
  
  so finally, 7!/2! * 8!/3!2!2!
• 5 years agoHelpfull: Yes(0) No(0)
• 9!/3!*2!*2!*2!=7560
• 5 years agoHelpfull: Yes(0) No(0)
• Ans: 13440
  Count where two n's are together = Total arrangements - where the n's are not together
  
  Total arrangements = 10!/(3!*3!*2!*2!) = 25200
  
  Now let us find the count where no two n's are together. For this n's can occupy the 8 positions which are represented by blanks.
  _ m _ m _ m _ p _ p _ q _ q _
  Out of these 8 positions, 3 positions can be chosen in 8C3 ways. In these 3 positions the three n's can be arranged in 8C3 * 3!/3! = 8C3 = 56 ways.
  The m,p,q can be arranged among themselves in 7!/(3!*2!*2!) = 210 distinct ways.
  So overall ways of arranging = 56*210 = 11760 ways.
  
  Hence number of ways in which two n's are together = 25200 - 11760 = 13440 ways
• 5 years agoHelpfull: Yes(0) No(0)