in how many ways can he letters of the english alphabet be arranged so that there are seven letters between the letters a and b and no letter is repeated

a)36*24!
b18*24!
c)24P7*2*18!
d)24P7*3*18!

• A -B or B - A --------------------> 2 WAYS
  from rest 24 letters, 7 can be arranged in 24P7 = 24! ways
  also position of A-------B can be 1-------9, 2--------10, ..., 18-------26 ( 18 ways )
  total no. of ways = 24P7 * 2 * 18! ways.
• 9 years agoHelpfull: Yes(29) No(5)
• answer is a) 36*24!
  let us ignore a and b so there will be 24! ways of arranging.
  now consider a - - - - - - - b as one and other 17 alphabets so its will be 18.
  we can also arrange a and b in 2! ways.
  so final answer will be : 24!*18*2= 24!*36.
• 8 years agoHelpfull: Yes(2) No(0)
• @ ANIBRATA HARI if a is at pos 1 b will at pos 9 and vice versa
  again if a is at 2 then b will ai pos 10
  3......................11
  4......................12
  5......................13
  6......................14
  7......................15
  like this when we reach 18 th pos if a is at 18 b will be at 26
  and 26 is our limit..........
  so,there are 18 ways again a and b can exchange position then 18*2 ways............and then *24P7 because 2 alphabets are used we are left with 24 and 7 position are there so 24P7
• 9 years agoHelpfull: Yes(1) No(0)
• can anyone explain how r these 18 ways r forming
• 9 years agoHelpfull: Yes(0) No(0)
• its coming 17! instead of 18! ?
• 9 years agoHelpfull: Yes(0) No(1)
• 13. A permutation is often represented by the cycles it has. For example, if we permute the numbers in the natural order to 2 3 1 5 4, this is represented as (1 3 2) (5 4). In this the (132) says that the first number has gone to the position 3, the third number has gone to the position 2, and the second number has gone to position 1, and (5 4) means that the fifth number has gone to position 4 and the fourth number has gone to position 5. The numbers with brackets are to be read cyclically. If a number has not changed position, it is kept as a single cycle. Thus 5 2 1 3 4 is represented as (1345)(2). We may apply permutations on itself If we apply the permutation (132)(54) once, we get 2 3 1 5 4. If we apply it again, we get 3 1 2 4 5 , or (1 2 3)(4) (5) If we consider the permutation of 7 numbers (1457)(263), what is its order (how many
  7541263
  3467152
  2653741
  2542367.....
  .
  ;
  7541263
  in 12th permutation
  
• 9 years agoHelpfull: Yes(0) No(1)