In how many ways can the letters of the English alphabet be arranged so that there are seven letters between the letters A and B, and no letter is repeated.

• 24c7*7!*2!
• 11 years agoHelpfull: Yes(59) No(27)
• A_ _ _ _ _ _ _ B and remaining 17
  So moving this A and B 1 step to the right . still we have 7 letters in between.
  So A and B can be shifted in the same manner to 18 more places.
  Now SAME CAN BE APPLICABLE TO B_ _ _ _ _ _ _A SO 18 HERE.
  NOW REMAINING ALPHABET ARE 24.
  -> 18*2*24!
  I.E. --> 36*24!
• 10 years agoHelpfull: Yes(59) No(23)
• no. of ways of choosing 7 letters out of 24=24c7
  no of ways of placing 7 letters w/o repitition=7!
  no of ways of arranging 2 letters A and B= 2!
  total no of ways=(24c7)*7!*2!
• 10 years agoHelpfull: Yes(27) No(10)
• We can fix A and B in two ways with 7 letters in between them. Now 7 letters can be selected and arranged in between A and B in 24P7 ways. Now Consider these 9 letters as a string. So now we have 26 - 9 + 1 = 18 letters
  These 18 letters are arranged in 18! ways. So Answer is 2 x 24P7 x 18!
  Infact, 2 x 24P7 x 18! = 36 x 24!.
• 9 years agoHelpfull: Yes(20) No(2)
• There are P(24,7) arrangements of the letters of the alphabet (excluding A and B)taken ten at a time, and hence 2*P(24,7) strings of 9 letters, each beginning and ending with an a and
  b(either letter coming first in a string).
  For each of these strings, there are 18 ! ways to arrange the 17 remaining letters and the string.
  So there are altogether 2*P(24,7)*18 ! arrangements of the desired type.
• 10 years agoHelpfull: Yes(16) No(5)
• ans will be 24!*2*18
• 11 years agoHelpfull: Yes(10) No(11)
• 24p7*2!*18!
  2! because AB are interchangeable
  24p7 to select 7 alphabets out of 24 alphabets
  18! because we hace considered the 9 letters set as one letter and arranged rest of the letters
  hence 24p7*2!*18!
• 9 years agoHelpfull: Yes(9) No(5)
• 24p7*2!
  out of 24 we have to opt 7 letters(26-A&B)
  and 2! for A&B
• 9 years agoHelpfull: Yes(6) No(3)
• 24c7 *7!*2!
• 11 years agoHelpfull: Yes(5) No(2)
• Answer: 36 * 24! or 24P7 * 2 * 18!
  Explanation:
  We can fix A and B in two ways with 7 letters in between them. Now 7 letters can be selected and arranged in between A and B in 24P7 ways. Now Consider these 9 letters as a string. So now we have 26 - 9 + 1 = 18 letters
  These 18 letters are arranged in 18! ways. So Answer is 2 x 24P7 x 18!
  Infact, 2 x 24P7 x 18! = 36 x 24!. So go for Option B as it was given as OA.
  
• 9 years agoHelpfull: Yes(5) No(0)
• Excluding A and B, there is a total of 24 letters in the alphabet. Out of that, 7 letters are to be selected and arranged between them. Thus to select and arrange 7 letters from 24 letters ==> 24P7 and so now we have arranged 9 letters including A and B.
  The remaining 17 letters can be arranged in 17! ways.
  But it is not necessary that A is in the 1st position followed by 7 letters and B is in the 9th position.B can be anywhere from the 9th position to the last 26th position like
  A_ _ _ _ _ _ _ B _ _ _ _ _ _ upto 26th.... , _A _ _ _ _ _ _ _ B _ _ _ _ upto 26th...., and so on. Thus there are 18 ways to fill the letters A and B.
  
  And finally it is also not necessary that A must be before those 7 letters and B after them. It can also be as B followed by those 7 letters followed by A.(B_ _ _ _ _ _ _A_ _....) . Thus there are two ways of arranging them.
  
  To conclude the total number of ways is,
  24P7 * 17! * 18 * 2!
  ==> 24! / (24-7)! * 17! * 36
  Total ways = 24! * 36
• 8 years agoHelpfull: Yes(3) No(0)
• total ways=22*21*20*19*18*17*16*15*14*2
  2 ways for changing the position of A and B
• 11 years agoHelpfull: Yes(2) No(9)
• ans is 2*sqrt(2)/3
  
• 11 years agoHelpfull: Yes(2) No(13)
• 24p7*2*18!
  
• 9 years agoHelpfull: Yes(2) No(2)
• We can fix A and B in two ways with 7 letters in between them. Now 7 letters can be selected and arranged in between A and B in 24P7 ways. Now Consider these 9 letters as a string. So now we have 26 - 9 + 1 = 18 letters
  These 18 letters are arranged in 18! ways. So Answer is 2 x 24P7 x 18!
  Infact, 2 x 24P7 x 18! = 36 x 24!
• 9 years agoHelpfull: Yes(2) No(0)
• A_ _ _ _ _ _ _ B
  
  first place= 22
  second plac=21
  third=20
  .
  .
  .
  seventh=14
  total ways= 22*21*20*19*18*17*16*15*14
• 11 years agoHelpfull: Yes(1) No(13)
• 2*18*24!
  
  2 because a,b and b,a
  24! because except a and b other can select any place
  18 because group a-b can place in 24 by 18 ways
• 10 years agoHelpfull: Yes(1) No(3)
• 24c7*7!*2!
• 9 years agoHelpfull: Yes(1) No(1)
• 2 x 24P7 x 18!
• 9 years agoHelpfull: Yes(1) No(0)
• 24p7*2 ... is correct answer
• 9 years agoHelpfull: Yes(1) No(0)
• 24c7*7!*2*18!
• 9 years agoHelpfull: Yes(1) No(0)
• can anyone give its proceedings..??
  
• 10 years agoHelpfull: Yes(0) No(1)
• only gopal amreliya is correct .all other answers are wrong including first one
• 10 years agoHelpfull: Yes(0) No(1)
• 24*23*22*21*20*19*18
• 9 years agoHelpfull: Yes(0) No(0)
• sorry forgot to mention about the a&b they also can interchange so..24c7*7!*18!*2!=36*24!
• 9 years agoHelpfull: Yes(0) No(0)
• 26 P 7=26!/19!
  there are 26 letters in English alphabet
  only 7 letters should be between A and B
  so it can be solved by using permutation.
• 9 years agoHelpfull: Yes(0) No(0)
• This is not a question in "Blood Relation" topic !!!!!
• 9 years agoHelpfull: Yes(0) No(0)
• A can be at 1st position and B can be at 9th position,A can be at 2nd position then B can be at 10th position and so on...
  this can be arrange in 18 ways
  a and b can be arrange in 2 ways
  and rest 24 alphabet can be arrange in 24!
  so answer can be given as 2*18*24!
• 9 years agoHelpfull: Yes(0) No(0)
• We can fix A and B in two ways with 7 letters in between them. Now 7 letters can be selected and arranged in between A and B in 24P724P7 ways. Now Consider these 9 letters as a string. So now we have 26 - 9 + 1 = 18 letters
  These 18 letters are arranged in 18! ways. So Answer is 2 x 24P724P7 x 18!
  Infact, 2 x 24P724P7 x 18! = 36 x 24!. So go for Option B as it was given as OA.
• 8 years agoHelpfull: Yes(0) No(0)
• Now the remaining number of letters are 24. Next we have to select 5 from 24 i.e no of ways of selection and arranging is 24C5*5! .A and B can be arranged at either sides so two ways of arranging A and B.
  Therefore total no of ways=24C5*5!*2
• 7 years agoHelpfull: Yes(0) No(0)