If the different permutations of the word EXA | vedclass

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Question

(B) The word $EXAMINATION$ consists of $11$ letters: $A, A, E, I, I, M, N, N, O, T, X$.To find the number of words before the first word starting with

Vedclass · Accepted Answer

$907200$

Vedclass · Answer

(B) The word $EXAMINATION$ consists of $11$ letters: $A, A, E, I, I, M, N, N, O, T, X$.To find the number of words before the first word starting with $E$,we must count all words starting with $A$.If we fix $A$ at the first position,we are left with $10$ letters: $A, E, I, I, M, N, N, O, T, X$.In these $10$ letters,$I$ occurs $2$ times and $N$ occurs $2$ times.The number of permutations of these $10$ letters is given by $\frac{10!}{2!2!}$.Calculation: $\frac{10 	imes 9 	imes 8 	imes 7 	imes 6 	imes 5 	imes 4 	imes 3 	imes 2 	imes 1}{2 	imes 2} = 907200$.Therefore,there are $907200$ words starting with $A$,which appear before any word starting with $E$ in the dictionary.

If the different permutations of the word $EXAMINATION$ are listed as in a dictionary,how many items are there in this list before the first word starting with $E?$

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