Six friends (all different people), including Meena and Sonu, are to stand in a straight line for a photograph. In how many ways can they stand if Meena and Sonu must always stand next to each other?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 240
People who must stay together are tied into one block; the block is arranged with the others, then the people inside the block.
Block (Meena + Sonu) + 4 other friends = 5 units, arranged in \(5!=120\) ways
Inside the block: Meena-Sonu or Sonu-Meena, \(2!=2\) ways
Ways \(=120\times2=240\)
Why the other options are incorrect
Option (1) 120 — Incorrect. This is only \(5!\); it leaves out the 2 orders of Meena and Sonu inside the block.
Option (2) 720 — Incorrect. This is \(6!\), all the ways, including those where the two are apart.
Option (3) 480 — Incorrect. This is \(720-240\), the ways in which Meena and Sonu are not next to each other.