Solution:

To select 4 letters from the word `EXAMINATION', we will use the combination formula.

Formula:

nCr = n! / r! (n-r)!

where, n = total number of items, r = number of items to be selected

Using the formula, we get:

10C4 = 10! / 4! (10-4)! = 10! / 4! 6! = (10 × 9 × 8 × 7) / (4 × 3 × 2 × 1) = 210

Therefore, there are 210 ways to select 4 letters from the word `EXAMINATION'.

But we need to consider the repetition of letters in the word `EXAMINATION'. To do this, we will use the permutation formula.

Formula:

nPr = n! / (n-r)!

Using the formula, we get:

4 letters can be selected from the word `EXAMINATION' in 10P4 = 10! / (10-4)! = 10! / 6! = (10 × 9 × 8 × 7) / (4 × 3 × 2 × 1) = 5040 / 24 = 210 ways.

But we need to subtract the permutations with repeated letters. The word `EXAMINATION' has 2 A's, 2 I's, and 2 N's.

So, the total number of permutations with repeated letters = 2! × 2! × 2! = 8

Therefore, the number of ways to select 4 letters from the word `EXAMINATION' without repetition = 210 - 8 = 202.

Hence, the correct option is (d) none of these.

Note: The question is asking for the ways of selecting 4 letters without repetition, but the options given are for selecting 4 letters with repetition.

125=5+24+1+13+9+14+1+20+9+15+14(E+X+A+M+I+N+A+T+I+O+N)