In how many ways can the letters of english alphabets is arranged so that there are 7 letters between the letters A & B and no letter is repeated?

• 24p7*2*18 ! thnik so
• 9 years agoHelpfull: Yes(10) No(0)
• if A & B both can be changed too then
  24*23*22*21*20*19*18*2
• 9 years agoHelpfull: Yes(6) No(0)
• A_ _ _ _ _ _ _ B here we fixed the position of A and B
  total no of alphabets is= 26
  remaing is= 24
  without repeting
  24*23*22*21*20*19*18
  
  
• 9 years agoHelpfull: Yes(5) No(1)
• we select 7 letters from 26-2(exclude a,b)
  so we select 24p7 ways
  and we arraged in 2 ways(start with either a or b)
  reamining 18 in 18! ways
  finally 24p7*2*18!
• 9 years agoHelpfull: Yes(5) No(0)
• If A is at first position B should be at 9th position,
  If A is at second position B should be 10th position,
  ---------- this can be done in 18 ways. and A and B can interchange their positions in 2 ways.
  remaining 24 letters can be arranged in 24! ways.
  
  So final answer is 2*18*24! = 36*24!
• 9 years agoHelpfull: Yes(5) No(1)
• 24p7 * 2 is the answer
• 9 years agoHelpfull: Yes(4) No(0)
• 8791595366400
• 9 years agoHelpfull: Yes(2) No(1)
• in between A & B 7 digit so (24c1x23c1x22c1x21c1x20c1x19c1x18c1)x2 because of B & A and 26-2=24 since no repetation.
• 9 years agoHelpfull: Yes(1) No(0)
• A)=====>18*2*24!
• 9 years agoHelpfull: Yes(1) No(0)
• can u expiain dt
  
• 9 years agoHelpfull: Yes(0) No(0)
• 24*23*22*21*20*19*18
• 9 years agoHelpfull: Yes(0) No(1)
• source: internet
  purpose: ease of understanding
  
  Arranging the words of waiting in Alphabetical Order : A,G,I,I,N,T,W
  
  Start with A_ _ _ _ _ _ This can be arranged in 6!/2! ways=720/2=360 ways
  so can't be arranged starting with A alone as it is asking for 32nd word so it is out of range
  
  AG_ _ _ _ then the remaining letters can be arranged in 5!/2! ways so,120/2=60 ways. Out of range as it has to be within 32 words.
  AGI _ _ _ Now the remaining letters can be arranged in 4! ways =24
  AGN _ _ _ _ can be arranged in 4!/2! ways or 12 ways
  so,24+12 =36th word so out of range. So we should not consider all the words start with AGN
  now AGNI_ _ _can be arranged in 3! ways =6 ways
  so 24+6=30 within range
  Now only two word left so, arrange in alphabetical order.
  AGNTIIW - 31st word
  AGNTIWI - 32nd word
  Read more at http://www.m4maths.com/placement-puzzles.php?SOURCE=tcs#v9mlPoEcfSTq3P6I.99
• 9 years agoHelpfull: Yes(0) No(3)
• 24p5*2 will be the answer, as total 26 alphabets, and 2 are fixed like A _ _ _ _ _ B or B _ _ _ _ _ A, so 26-2=24 letter can be represented in 5 places in 24p5 ways, and as it could start with either A or B. so the answer will be (24p5*2),, here we are multiplying by 2 as 2p2=2.
• 9 years agoHelpfull: Yes(0) No(0)
• 24c7*7!
  as there are only 24 alphabets now so we select 7 outta them and those 7 can be permuted in 7! ways!!
• 9 years agoHelpfull: Yes(0) No(0)
• A( QWERTYU)B IOPLKJHGFDSZXCVNM
  A and B can be arranged in 2! ways.
  Now 24 remaining
  letters between A and B (QWERTY) can be arranged in 24P7 ways.
  remaining 18 letters can be arranged in 18! ways.
  so answer is 2* 24P7*18!
• 9 years agoHelpfull: Yes(0) No(0)
• from where this 18! came? i mean after selecting 7 from 24, 17 alphabets r left and moreover we hav to choose 7 alphabets only
  can anyone tell??
• 9 years agoHelpfull: Yes(0) No(0)
• remaining 18 means remaining 17 letters +1 (9 letters we already selected should be taken as 1)=18
• 9 years agoHelpfull: Yes(0) No(0)
• we can arrange A n B in 18*2! ways
  n there can be letters in 7 places b/w A n B arranged as 24p7
  ans is 24p7 *18*2
• 9 years agoHelpfull: Yes(0) No(0)