In how many ways can the letters of the english alphabet be arranged so that there are seven letter between the letters A and B, and no letter is repeated
a. 24P7 * 2 * 18! b. 36 * 24!
c. 24P7 * 2 * 20! d. 18 * 24!

• Answer : B. 36*24!
  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 Option B is Correct.
• 9 years agoHelpfull: Yes(8) No(0)
• ans.b 36*24!
  
• 9 years agoHelpfull: Yes(7) No(2)
• ans 24P7*2*18!
• 9 years agoHelpfull: Yes(7) No(4)
• ans is B. 36*24!
• 9 years agoHelpfull: Yes(6) No(1)
• ans is a
  
  we have total 26 alphabets but two are already given so only 24 left so arranging these 24 in 24p7 ways. Now given A and B can also be arranged in two ways and then the remaining 18 can be arranged in 18! ways.
• 9 years agoHelpfull: Yes(4) No(2)
• 24p7*2!*18
• 9 years agoHelpfull: Yes(1) No(3)
• 24C7 7! 2! 17! 18
  select 7 out of 24 (26-2, 2 is for a and b). keep a, b and the selected 7 in a box. arrange the 7 between a and b in 7! ways. you can have a in the beginning and b at end or vice versa. Hence 2! for that. arrange remaining 17 in 17! ways. put the box of a, b and 7 letters at any place b/w the 17 letters in 18 ways.
• 9 years agoHelpfull: Yes(1) No(3)