**Concept:** The question tests on the basics of Counting

**Solution**

The distinct letters in EXAMINATION are E, X, A, M, I, N, T and O which are 8 letters with A, I and N being repeated twice.

(a) Number of distinct 4 letter words that can be formed = 8P4 = 8!/(8 - 4)! = 8 * 7 * 6 * 5 = 1680 words

(b) Number of words where 2 letters are repeated and 2 are distinct --> Choose 1 out of 3 for the 2 repeated letters in 3C1 ways

Choose 2 letters from the remaining 7 letters in 7C2 ways.

Total such words = 3C1 * 7C2 * (4!/2!) = 3 * (7 * 6/ 2) * (4 * 3) = 756

(c) Number of words with 2 letters being repeated twice.

Choose 2 letters out of 3 in 3C2 ways. Then arrange them in (4! / 2!2!) ways = 3 * (4 * 3 * 2 / 2 * 2) = 18 ways

Total number of words = 1680 + 756 + 18 = 2454

Option C