There are 6 letters in the word INDIAN in which I and N are repeated twice. Number of different words that can be formed using the letters of the word INDIAN = \(\frac{6!}{2!2!}\) = \(\frac{6\times5\times4\times3\times2!}{2\times2!}\) =180
When two N’s are together. Let us consider the two N’s as one unit. They can be arranged with 4 other letters in \(\frac{5!}{2!}=\frac{5\times4\times3\times2!}{2!}\) = 60 ways.
∴ 2 N can be arranged in \(\frac{2!}{2!}\) = 1 way.
∴ Required number of words = 60 x 1 = 60
