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# If the different permutations of all the letters of the word EXAMINATION are listed as in dictionary,how many words are there in this list before the first word starting with E?

$\begin{array}{1 1}(A)\;907200\\(B)\;917200\\(C)\;926200\\(D)\;93630\end{array}$

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• $n!=n(n-1)(n-2).....(3)(2)(1)$
Words starting with A are formed with the letters 2I's,2N's A,E,X,M,T,O
Numbers of words formed by these letters $=\large\frac{10!}{2!2!}$
$\Rightarrow \large\frac{10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{2\times 2}$
$\Rightarrow 10\times 9\times 8\times 7\times 6\times 5\times 3\times 2\times 1$
$\Rightarrow 907200$
Then the words starting with $E,I,M,N,O,T,X$ will be formed.
$\therefore$ Number of words before the first word starting with E is formed
$\Rightarrow 907200$
Hence (A) is the correct answer.

+1 vote