Easy P&C! :)
Probability
Level
pending
The letters of the word AGAIN are permuted among themselves. If these words are written as in a dictionary, what will be the fiftieth word?
NOTE: This problem is not original.
NAAGI
GAAIN
IAGNA
NAAIG
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1 solution
Number of words beginning with A : (A _ _ _ _ .) are = 4!=24.
Number of words beginning with G : (G _ _ _ _ .) are = 4!/2!=12.
(2! appears as the words with the two A's swapped are the same.)
Number of words beginning with I : (I _ _ _ _ .) are = 4!/2!12.
The first 48 words begin with A, G or I.
Thus, the 49th word begins with N and is NAAGI and the fiftieth word will be NAAIG.