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Question
If the letters of the word 'LATE' be permuted and the words so formed be arranged as in a dictionary, find the rank of the word LATE.
Solution
In a dictionary, the words are listed and ranked in alphabetical order. In the given problem, we need to find the rank of the word LATE.
For finding the number of words starting with A, we have to find the number of arrangements of the remaining 3 letters.
Number of such arrangements = 3!
For finding the number of words starting with E, we have to find the number of arrangements of the remaining 3 letters.
Number of such arrangements = 3!
For finding the number of words starting with L, the next alphabetical letter would be A, followed by E and then T, i.e. LAET.
The next alphabetical word would be LATE.
Number of words after which we reach the word LATE = 3!+3!+1+1 = 14
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