The number of different ways in which 8 persons can stand in a ro… - Vidyadip

MCQ

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:

✓
60 × 5!
B
15 × 4! × 5!
C
4! × 5!
D
None of these.

✓

Answer

Correct option: A.

60 × 5!

60 × 5!

Solutions:
The four people, i.e A, B and the two persons between them are always together. Thus, they can be considered as a single person. So, along with the remaining 4 persons, there are now total 5 people who need to be arranged. This can be done in 5! ways. But, the two persons that have to be included between A and B could be selected out of the remaining 6 people in ${ }^6 P_2$ ways, which is equal to 30. For each selection, these two persons standing between A and B can be arranged among themselves in 2 ways.
$\therefore$ Total number of arrangements = 5! × 30 × 2 = 60 × 5!

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