(a, b, c )

INTERMEDIATE has 3E’s, 2I’s and 2 T’s and A, D, M, N, R one each, thus total of 12 letters. If words start with I and end with E i.e. I x x x x x x x x x x E; the ten places (shown by cross) has to be filled with 2 E’s and 2 T’s and 6 distinct letters.

∴ Number of words = = 907200

If vowels and consonants occupy their original places, then 6 vowels (E, E, E, I, I, A) can be arranged in at their original places.

6 consonant (N, T, T, M, D, R) can be arranged in at their original place.

∴ Number of words = × = 21600

If vowels and consonants occur together, then 6 vowels can be arranged in 6 places in
. E × E × E × I × I × A

6 consonants can be arranged in 5 places shown be crosses and one place either extreme left or extreme right in × 2!.

∴ Number of words = × × 2! = 43200

If all the vowels occur together, then group of 6 vowels taken together will be considered one and 6 consonants can be arranged in ways.

[There are two T’s]. But 6 vowels can be arranged in ways.

∴ Number of words = × = 151200