Q. 20

# 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, isA. 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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