$\mathrm{EXAMINATION}$ શબ્દના તમામ ભિન્ન ક્રમચયોને જો શબ્દકોષ પ્રમાણે ગોઠવી યાદી બનાવવામાં આવે તો પ્રથમ શબ્દ $\mathrm{E}$ થી શરૂ થાય તે શબ્દ પહેલા કેટલા શબ્દો હશે ?

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 $A=\frac{10 !}{2 ! 2 !}=907200$

Thus, the required numbers of words is $907200 .$