in how many ways can letter of word MOBILE can be arranged so that atleast two consonant remains together

• Ans.-144
  No. of ways to select 2 consonants from 3=3C2
  no. of ways to arrange these two consonants= 3C2*2!
  no. of ways to arrange remaining terms=4!
  Hence, total no. of ways to arrange= 3C2*2!*4!=144
• 8 years agoHelpfull: Yes(26) No(9)
• ans is 576
  (total number of arrangements)-(arranging no two consonants to be together)
  6!-(4p3*3!)=720-144=576
• 8 years agoHelpfull: Yes(18) No(6)
• If atleast 2 consonant has to come together
  then
  
  1st case MB will come together i.e. MB*O*I*L*E = 5!=120
  
  2nd case MBL will come together i.e. MBL*O*I*E =4!=24
  
  120+24=144
• 8 years agoHelpfull: Yes(9) No(4)
• Total number of ways - no consonants to be together
  =6! - 3!*4*3*2= 720-144
  =576
• 8 years agoHelpfull: Yes(9) No(0)
• 5!2!*3=720
  4!3!=144
  720+144=864
  
• 8 years agoHelpfull: Yes(6) No(2)
• The word 'MOBILE' has
  6
  6 letters in which there are
  3
  3 vowels and
  3
  3 consonants. Every letter is distinct.
  
  Total number of arrangements possible using the letters of the word 'MOBILE'
  =
  6
  !
  =6!
  
  Now find out the different arrangements where no consonants are together.
  For this, arrange
  3
  3 vowels in
  3
  !
  3! ways.
  There are
  4
  4 positions now to place the
  3
  3 consonants and this can be done in
  4P3
  4P3 ways.
  => Different arrangements where no consonants are together
  =
  3
  !
  ×
  4P3
  =3!×4P3
  
  Therefore, different ways in which the word 'MOBILE' can arranged so that at least 2 consonants come together
  =
  6
  !
  −
  3
  !
  ×
  4P3
  =
  720
  −
  (
  6
  ×
  24
  )
  =
  720
  −
  144
  =
  576
  =6!−3!×4P3=720−(6×24)=720−144=576
  
• 8 years agoHelpfull: Yes(5) No(2)
• Case 1:Taking only MB together
  MB can be arranged in 5 ways and remining are arranged(along with MB ) in 4! ways.
  And also MB can be arranged in 2 ways.
  so the no.of ways are 5*4!*2 =>5!*2 =>120.
  
  2nd case: taking MBL
  MBL can be arrangd in 4 ways and remining(along with MBL) are arranged in 4*3! ways
  MBL can be arranged in 3! ways
  so the total no ways are:4!*3! => 144
  
  Adding 2 cases the total no. of way are 144+240=384.
• 8 years agoHelpfull: Yes(5) No(2)
• Answer: 384
  Explanation: Two possible cases: Two consonants together + Three consonants together
  5! x 2! + 4! x 3! = 384
  
• 8 years agoHelpfull: Yes(5) No(5)
• the ans ll be 576 only
  
• 8 years agoHelpfull: Yes(4) No(2)
• they said at least two then we may arrange three together also then it is more than 144
• 8 years agoHelpfull: Yes(3) No(1)
• Guys don't be confused, Think smartly.. You can easily solve it.
  Total no.of ways(6!) - NO two cnsnt together(144) = 576
• 8 years agoHelpfull: Yes(2) No(0)
• When MB is together and is definitely separated from L...then no of ways 4C2*2!*3!*2!=144
  This can be done in 3 ways(mb,bl,lm)
  So no ways =144*3=432
  
  Now taking MBL together definitely, 4*3!*3!=144
  
  So total no of ways=144+432=576
• 7 years agoHelpfull: Yes(2) No(0)
• 180
  there is two case when only 2 consonats(144) take together and other one is when 3 consonants take together(36) total=180
• 8 years agoHelpfull: Yes(1) No(2)
• Answer is 384
  2consonent together + 3consonent together
  5!*2!+4!*3!
• 8 years agoHelpfull: Yes(1) No(2)
• total words 6 so 6!
  now ques has given that atleast 2 constant and question contain 3 vowels so this vowel can occupy remaining any 4 places so ,
  6! - (3!*4P3)= 720-144=576.
• 8 years agoHelpfull: Yes(1) No(0)
• Ans=Total no of arrangements-No of arrangements where no consonants are together
  
  Total no of arrangements= Since all the letters are distinct so that we can arrange MOBILE 6! ways
  
  Total no of arrangements where no consonants are together ,arrangement will look like this
  
  _O_I_E_
  So three vowels can be arrange like this in (3P3)3! ways and the remaining Four places can be filled by 3 consonants in 4P3 ways
  so total arrangements where no consonants are together is 3!*4P3
  so the answer is 6!-(3!*4p3)=576
• 8 years agoHelpfull: Yes(1) No(1)
• 123456 positions
  let us take 12 positions are costent n can be with consonents.They can be arranged in 3c2*2! ways
  the other 4 positions arranged in 4! ways.
  so 3c2*4!*2!=144 ways
• 8 years agoHelpfull: Yes(0) No(3)
• No of arrange way of consonant is=3!+1!=4!
  No of arrange way of consonant remain together is=3p2=3!
  Total no of way of arrange letter is=4!*3!=144
• 8 years agoHelpfull: Yes(0) No(1)
• SRUTHI PUJARI
  can u explain ?
  how 4p3*3!
• 8 years agoHelpfull: Yes(0) No(0)
• ((total letters - no of consonant + 1 )! / (no of times any vowels are repeat)! ) * (( no of consonant)! / (no of times any consonant are repeat)!
  =(6-3+1)! * 3! [ here, no letters are repeated, so no of times repeatation we need not to calculate]
  =144
• 8 years agoHelpfull: Yes(0) No(2)
• case 1:when 2 consonants are together(i.e. may be MB,BM,LM etc)
  no. of way of arrangement among two consonants=3P2
  no. of way of arranging this pair along the other letters of the word=5P5
  
  Case 2: :when 3 consonants are together(i.e. may be MBL,BML,BLM etc)
  no. of way of arrangement among 3 consonants=3P3
  no. of way of arranging these 3 along the other letters of the word=4P4
  
  so, total no. of ways=( 3P2*5P5)+(3P3*4P4)=720+144=864
• 7 years agoHelpfull: Yes(0) No(0)
• ans = 576
  total no of ways - when no consonant are together
  there are total 6 letters so we can arrange them in 6! ways = 6!=720
  when no consonant are together then it looks like
  _o_i_e_
  o, i,e can be arranged in 3! ways
  now remaining 4 positions and 3 consonant i.e. = 4P3 ways = 24
  so 3!*24= 6*24
  =144
  so ans = 720-144=576
  guys this is the correct answer, plz do not confuse others.
• 5 years agoHelpfull: Yes(0) No(0)
• in first place we take 2 consonant as fixed and they can interchange its place and remaining 4 place have 4 letters left and they can inter change so the solution is ,
  
  3P2*4P4 = 6*24=144
• 2 years agoHelpfull: Yes(0) No(0)
• No(4)Total number of ways - no consonants to be together
  =6! - 3!*4*3*2= 720-144
  =576
• 1 year agoHelpfull: Yes(0) No(0)