Mark the correct alternative in the following:
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, is
A. 60 × 5!
B. 15 × 4! × 5!
C. 4! × 5!
D. none of these
As, it is required that, two particular persons A and B there are always two persons so, let us consider this arrangement be “A××B” and consider it as a single object.
So, we are left with, 4 persons and an object, i.e. total 5 objects.
Now, this 5 objects can be arranged in 5! ways.
Again, the two ‘×’ are to be filled with 2 persons from 6 persons, this can be done in 6P2 = 30 ways.
Two persons ‘A’ and ‘B’ can be arranged in 2! = 2 ways.
So, the total 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, is
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