In how many different ways can letters of the word “REASONING” be arranged?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 181440
If \(n\) letters are arranged and one letter occurs \(r\) times, swapping the copies of that letter gives no new word, so the number of arrangements is \(\frac{n!}{r!}\).
REASONING has 9 letters: R, E, A, S, O, N, I, N, G, with N twice and every other letter once
Arrangements \(\displaystyle =\frac{9!}{2!}=\frac{362880}{2}=181440\)