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Question
If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?
Solution
In the given word EXAMINATION, there are 11 letters out of which, A, I, and N appear 2 times and all the other letters appear only once.
The words that will be listed before the words starting with E in a dictionary will be the words that start with A only.
Therefore, to get the number of words starting with A, the letter A is fixed at the extreme left position, and then the remaining 10 letters taken all at a time are rearranged.
Since there are 2 Is and 2 Ns in the remaining 10 letters,
Number of words starting with A = `(10!)/(2!2!)` = 907200
= `(10 xx 9 xx 8 xx 7 xx 6 xx 5 xx 4 xx 3 xx 2 xx 1)/4`
= 907200 By arranging the given letters like the letters in the dictionary, the next letter will be E.
∴ Number of words formed before E = 907200
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