The number of different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always two persons?
let the row be like that
A 1 2 B 3 4 5 6
let underline person be consider as one then the total no. of ways in which line can form is 5 !
now there are 2 place between A and B in which any two person can sit out of 6 so the no.of way to do that is P(6 , 2) = 6! / ( 6 -2 )! = 30
A and B can be arrange in 2! ways
the total no of ways is = 120 * 30 * 2 = 7200
A 1 2 B 3 4 5 6
let underline person be consider as one then the total no. of ways in which line can form is 5 !
now there are 2 place between A and B in which any two person can sit out of 6 so the no.of way to do that is P(6 , 2) = 6! / ( 6 -2 )! = 30
A and B can be arrange in 2! ways
the total no of ways is = 120 * 30 * 2 = 7200