The total number of permutations of 4 letters that can be made out of the 

letters of the word EXAMINATION, is

We have, 11 letters, $A, A; i, i; N, N; E, X; M; T;O.$

For groups of 4 we way arrange these as follows:

(i) Two alike, two others alike 

(ii) Two alike, two different 

(iii) All four different.

(i) gives rise ${\mathrm{C}}_2$ selections,

(ii) gives rise $3{\times }^7{C}_2$ selections and

(iii) gives rise ${ }^8{\mathrm{C}}_4$ selections.

So, the number of permutations 

$=3\frac{4!}{2!2!}+63\frac{4!}{2!}+70\left(4!\right)=2454.$