"LEADING" arrange it in such a way that atleast two vowels always together...??

• 3c2*(6!*2!) + 3c3*(5!*3!)
  
• 11 years agoHelpfull: Yes(55) No(5)
• There are 2 possiblities i.e.
  1) Either all the three vowels will come together
  2) Or 2 vowels will comes together
  
  for 1st condition LONG "EAI" = LONG with "EAI" can arrange in !5 ways and then "EAI" can arrange in !3 ways therefore !5 * !3 = 120*6=720
  
  Now same for the second 1 LONGI "EA" can arrange in !6 possible ways but "EA" only can arrange in !2 ways and therefore !6*!2= 720* 2= 1440
  
  Now the total no. of ways of arranging these 2 = 1440+720= "2160"
  
  Ans = 2160
• 11 years agoHelpfull: Yes(47) No(31)
• in LEADING there are 3 vowels.
  if 2 vowels fix then arrangement will be 6!*2!
  if 3 vowels fix then arrangement will be 5!*3!
  now total ways will be (6!*2!)+(5!*3!)=2160 ans
• 11 years agoHelpfull: Yes(28) No(5)
• (6!*2!*3)+(5!*3!)=5040
• 11 years agoHelpfull: Yes(25) No(2)
• (total)- (no two vowels come together)
  total=7!
  no two vowels come together={_L_D_N_G_)=4!*(5C3*3!)
  7!-(4!*5P3)=3600
• 11 years agoHelpfull: Yes(17) No(8)
• There are two possibilities :-
  1) Either all the three vowels will come together
  2) 2 vowels will come together
  
  Case 1 :- All three vowels come together
  If three vowels E,A & I come together they can taken as one group EAI
  now we have only 5 words to arrange i.e. L,D,N,G,EAI
  They can be arranged in 5!*3!=720 ways
  
  Case 2 :- Only two vowels come together
  
  In this case we have to select which two vowels come together in order to make them in one group
  
  this groups can be :- EA or AI or EI total 3 groups(3C2=3 groups)
  So, total ways for this case=3*6!*2!=4320.
  
  So.final ans is=4320+720=5040
  
• 10 years agoHelpfull: Yes(16) No(2)
• 6!2!+5!3!...????
• 11 years agoHelpfull: Yes(10) No(5)
• The word 'LEADING' has 7 different letters.
  
  When the vowels EAI are always together, they can be supposed to form one letter.
  
  Then, we have to arrange the letters LNDG (EAI).
  
  Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.
  
  The vowels (EAI) can be arranged among themselves in 3! = 6 ways.
  
  Required number of ways = (120 x 6) = 720.
  
• 11 years agoHelpfull: Yes(9) No(17)
• but prahar gupta in the case of two vowels come together here we can arrange the vowels in 3 ways LDNG+(A or E or I =LDNGA or LDNGE or LDNGI) and the reamining two vowel letters arrange it in two ways so 2! hence total 6!*2!*3+5!*3!
• 11 years agoHelpfull: Yes(7) No(1)
• here it is given that "at least" 2 vowels alwys toghtr so it can b 2 or three !! so if we will sbtract (total no of arrngmnt-no vowels togthr )we will get the answr . total no of arrngmnt=7!=5040 .
  and no of ways to arrnge s.t no vowels togethr=4!*5p3=1440.
  so ans=5040-1440= 3600
• 11 years agoHelpfull: Yes(6) No(2)
• 3600 is the right answer...
• 11 years agoHelpfull: Yes(3) No(1)
• 7!-3!*5! = 720
• 11 years agoHelpfull: Yes(2) No(6)
• 3c2*!2*!6+3c3*!3*!5
• 11 years agoHelpfull: Yes(2) No(1)
• LE'AI'DNG and L'EAI'DNG is the same permutation , when you consider two vowels in the first case and there vowels in the second case.
  
  So, 'three vowels together' appears in a 'two vowel together' word when the other vowel comes near the pair of vowels
  
• 11 years agoHelpfull: Yes(1) No(0)
• 36oo........7!-4!(5c3*3!)
• 11 years agoHelpfull: Yes(1) No(1)
• LEADING
  TAKE ANY TWO VOWELS
  (LDING)*(EA)
  6!=720
  NOW
  2! FOR TWO VOWELS
  2!=2
  TOTAL=720*2=1440
  
• 11 years agoHelpfull: Yes(1) No(1)
• Answer is 2160 !!!
• 11 years agoHelpfull: Yes(1) No(0)
• DEALING
  Two vowels E and A are together.
• 11 years agoHelpfull: Yes(0) No(8)
• we have to find no of arrangement
• 11 years agoHelpfull: Yes(0) No(2)
• atleast 2 and atleast 3 are two chances as there are 3 vowels
  so answer id (3p2 * 5!) + (3! *4!) = 864
• 11 years agoHelpfull: Yes(0) No(2)
• ans :- 2880
• 11 years agoHelpfull: Yes(0) No(2)
• 720
  5!=120
  then here are 3 vowels then arrange atleast two vowels always together so only 3 case are possible IE , EA, AI so 3!=6
  so total is 120*6=720
  
• 11 years agoHelpfull: Yes(0) No(2)
• Number of ways= 3P2*6!+3P3*5!
• 11 years agoHelpfull: Yes(0) No(1)
• 2160 is d ans
• 11 years agoHelpfull: Yes(0) No(2)
• =(6!*2!)+(5!*3!)
  =2160
• 11 years agoHelpfull: Yes(0) No(3)
• ans is 5!*3!=720
• 11 years agoHelpfull: Yes(0) No(2)
• 2160
  as 7!-(4!*5!)
  {total ways- ways having no two vowels together}
• 11 years agoHelpfull: Yes(0) No(0)
• since atleast 2 vowels should be together i.e either EI/AI/EA.
  Now for the first case EI---LADGN(EI)---5!2!5! (6! for total, then 2! for EI and 5! for LADGN)....similarly for AI and EA... so 2*5!2!5!
  
  then in case where 3 vowels are to be selected----LDNG(AEI)---5!4!3! (5! for total , 4! for LDNG and again 3! for AEI)..
  hence total ways (2*(5!2!5!))+ 5!4!3!
• 11 years agoHelpfull: Yes(0) No(0)
• i think it is=(5!*2!)+(6!*2!*3c2) bcz while taking 2 vowels at a time those two can be selected in 3 ways na....
• 11 years agoHelpfull: Yes(0) No(0)
• (AEI)LDNG,,,Take all vowels as one now total cases 5! and vowels position can also interchange with each other like 3!so(5!*3!)=720
• 11 years agoHelpfull: Yes(0) No(0)
• 6!*2! smple..consider only 2 vowels have to b together.
  
• 9 years agoHelpfull: Yes(0) No(0)
• 5!*3!+6!*2!=2160
• 9 years agoHelpfull: Yes(0) No(1)
• when i solved im getting 5040 ie.(5!*3!+(6!*3c2*2!)) . but its showing answer is 2160. which one is correct guys ?
• 9 years agoHelpfull: Yes(0) No(0)
• (lead)(eai)=5!*3!=720
  leada (ei)=6!*2=1440
  leadi (ea)=6!*2=1440
  leade (ai)=6!*2/2=720 as e is repeating in main so answer is 4320.
• 9 years agoHelpfull: Yes(0) No(0)
• There are 2 possiblities i.e.
  1) Either all the three vowels will come together
  2) Or 2 vowels will comes together
  
  for 1st condition LONG "EAI" = LONG with "EAI" can arrange in !5 ways and then "EAI" can arrange in !3 ways therefore !5 * !3 = 120*6=720
  
  Now same for the second 1 LONGI "EA" can arrange in !6 possible ways but "EA" only can arrange in !2 ways and therefore !6*!2= 720* 2= 1440 same for "EI" ans "AI"
  
  Now the total no. of ways of arranging these 2 = 1440*3+720= "5040"
  
  Ans = 2160
  
• 9 years agoHelpfull: Yes(0) No(0)
• Total possible arrangement = 7! = 5040
  total=7!
  when no 2 vowel comes together : {_L_D_N_G_)
  here 3 vowels can be placed in 5 positions and the vacant space will be removed so : 5p3 * 4! = 60*24 = 1440.
  So required arrangements : (5040 - 1440) = 3600
• 8 years agoHelpfull: Yes(0) No(1)
• 2160
  5!*3! +6!*2! =2160
• 5 years agoHelpfull: Yes(0) No(0)