Question

in how many ways can 3 letters out of five distinct letter A,B,C,D and E be arranged in a straight line so that A and B never come together?​

Answer 1

Answer:

Total number of ways in which 3 letters can be arranged is 5*4*3 = 60 ways

Total number of ways 3 letters can be arranged such that A and B are always together is  in  ways A and B can be arranged between themselves (2)*  of ways in which the remaining 3 letters can be picked (3) *  of ways in which the 3 letters and (A&B) can be arranged(2) = 3*2*2 = 12  

Therefore, the number of ways in which A and B are never together = 60 - 12 --> 48