In how many different ways can the letters of the word 'DELETE' be arranged?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 120
When a letter repeats, swapping the identical letters gives no new arrangement. So the arrangements of all the letters, \(n!\), are divided by the factorial of the number of times each letter repeats.
DELETE has 6 letters: D, L and T once each, and E three times
Arrangements \(\displaystyle =\frac{6!}{3!}=\frac{720}{6}=120\)
Tip: 720 (Option 1) is \(6!\), the count as if all six letters were different. It counts each word 6 times, once for every order of the three E’s.