In how many different ways can the letters of the word “MANAGEMENT” be arranged?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\frac{10!}{2!\,2!\,2!\,2!}\)
\(n\) letters can be arranged in \(n!\) ways when all are different. When a letter is repeated \(r\) times, swapping its copies gives the same word, so we divide by \(r!\) for each repeated letter.
MANAGEMENT has 10 letters: M, A, N, A, G, E, M, E, N, T
Repeated letters: M twice, A twice, N twice, E twice; G and T once each
Number of arrangements \(\displaystyle=\frac{10!}{2!\,2!\,2!\,2!}\)