In how many different ways can the letters of the word 'DELETE' be arranged?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 120
When some letters of a word repeat, swapping identical letters gives no new arrangement. So the total \(n!\) is divided by the factorial of the number of times each letter repeats.
DELETE has 6 letters: D, L, T once each and E three times
Arrangements \(\displaystyle =\frac{6!}{3!}=\frac{720}{6}=120\)
Tip: 720 (Option 4) is \(6!\), the count as if all six letters were different; it counts every arrangement 6 times, once for each order of the three E’s.