The six letters of SCHOOL are written in a row, each used once; the two O’s are identical. How many different rows have the two O’s next to each other?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 120
Letters that must stay together are tied into one block. Two identical O’s inside the block can stand in only one way.
SCHOOL has 6 letters: S, C, H, L once each and O twice
Block (OO) + S, C, H, L = 5 different units, arranged in \(5!=120\) ways
Inside the block: OO, only 1 way (the O’s are identical)
Arrangements \(=120\times1=120\)
Why the other options are incorrect
Option (1) 360 — Incorrect. This is \(\frac{6!}{2!}\), all the arrangements of SCHOOL, including those where the O’s are apart.
Option (2) 240 — Incorrect. This is \(5!\times2!\), which swaps the two O’s inside the block; they are identical, so the swap gives nothing new.
Option (4) 720 — Incorrect. This is \(6!\), which treats the O’s as different and ignores the condition.