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! , 15 × 4! × 5! , 4! × 5!, None of These. - Mathematics

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

Options

•  60 × 5!

• 15 × 4! × 5!

• 4! × 5!

• none of these.

Solution

60 × 5!
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 6P2 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.
∴ Total number of arrangements = 5! x 30 x 2 = 60 x 5!

Concept: Permutations
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Q 20 | Page 47