In how many different ways can all the letters of the word CANNON be arranged? (Each letter is used exactly once; the three N’s are identical.)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 120
When a letter appears \(p\) times, swapping its copies gives no new arrangement, so \(n!\) is divided by \(p!\).
CANNON has 6 letters: C, A, O once each and N three times
Arrangements \(\displaystyle =\frac{6!}{3!}=\frac{720}{6}=120\)
Why the other options are incorrect
Option (1) 720 — Incorrect. This is \(6!\), which treats the three N’s as different letters.
Option (3) 240 — Incorrect. This is \(\frac{6!}{3}\); the division must be by \(3!=6\), not by 3.
Option (4) 60 — Incorrect. This is \(\frac{6!}{3!\times2!}\), as if a second letter were repeated twice; only N repeats.