In how many different ways can letters of the word "DAIRY" be arranged?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 120
The word DAIRY has five different letters (no letter repeats), so every ordering of them gives a different arrangement. Filling the five places one by one:
The first place can take any of the 5 letters, the second any of the 4 left, then 3, 2 and 1
Number of arrangements: \(5\times4\times3\times2\times1=5!=120\)
In general, n different things can be arranged in n! ways; repeated letters would reduce the count, but DAIRY has none.