Explanation

(a)
The word EXAMINATION has 2A, 2I, 2N, E, M, O, T, X therefore 4 letters can be chosen in following ways
Case I When 2 alike of one kind and 2 alike of second kind is $\ ^{3}C_{2}$
$\therefore$ Number of words$= \ ^{3}C_{2} \times \frac{4!}{2!2!} = 18$
Case II When 2 alike of one kind and 2 different $ie$, $\ ^{3}C_{1} \times \ ^{7}C_{2}$
$\therefore$ Number of words$= \ ^{3}C_{1} \times \ ^{7}C_{2} \times \frac{4!}{2!} = 756$
Case III When all are different $ie$, $\ ^{8}C_{4}$
Hence, total number of words
$= 18 + 756 + 1680 = 2454$