Permutation
Probability
Level
2
If all the permutations of the letters of the word "AGAIN" are arranged as in Dictionary, then 50th word is
NAIAG
NAAGI
NAAIG
NAGAI
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1 solution
There are 5 letters but one letter has a repeating one, which is A. Therefore there are 5!/2! =60 ways of making a word. We want to find the 50th word. Alphabetically, starting with A, there are 4!/2! ways to form a word. Then, with the other A, there are another 4!/2! ways to form a word. Now, starting with G, there are 4!/2! ways to form a word. Now, starting with I, there are 4!/2! ways to form a word. So far, there are a total of 48 words alphabetically. Thus, the 49th word is NAAGI and the 50th word is NAAIG