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Find the number of distinct words formed from letters in the word INDIAN. How many of them have the two N’s together? |
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Answer» 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 |
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