Last updated at Jan. 30, 2020 by Teachoo
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Example 22 Find the number of words with or without meaning which can be made using all the letters of the word AGAIN. If these words are written as in a dictionary, what will be the 50th word? ‘AGAIN’ = 2A, 1G, 1I & 1N In dictionary, letters appear alphabetically, 4 letters in which A, G, I, N Since, we arrange 4 letters, Number of words = 4P4 = 4! = 24 4 letters in which 2A, I, N Since, letters are repeating, number of words = 𝑛!/𝑝1!𝑝2!𝑝3! Number of letter = n = 4 Since 2A, p1 = 4 Number of words = 4!/2! = 12 4 letters in which 2A, G, N Since, letters are repeating, number of words = 𝑛!/𝑝1!𝑝2!𝑝3! Number of letter = n = 4 Since 2A, p1 = 4 Number of words = 4!/2! = 12 Thus, Total no of words starting with A, G, & I = 24 + 12 + 12 = 48 Hence, 49th word will be start from N i.e. N A A G I & remaining four rearrange according to a dictionary Thus, The 50th word is N A A I G Hence the 50th word will be NAAIG
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