To find the number of words formed from the letters of the word EAMCET such that two vowels are never together, we can use the concept of permutations.

1. Identify the given letters:
The given word is EAMCET. It has 6 letters.

2. Identify the vowels:
The vowels in the word EAMCET are E and A.

3. Find the total number of words:
To find the total number of words that can be formed from the given letters, we need to find the permutations of all the letters.

Total number of words = 6!

4. Find the number of words with vowels together:
To find the number of words where the vowels are together, we can consider the two vowels (E and A) as a single entity and find the permutations of the remaining letters.

Let's consider EA as a single entity. So now we have 5 letters: (EA), M, C, E, T.

Number of words with vowels together = 5!

5. Find the number of words with vowels not together:
To find the number of words where the vowels are not together, we subtract the number of words with vowels together from the total number of words.

Number of words with vowels not together = Total number of words - Number of words with vowels together
= 6! - 5!

6. Calculate the final answer:
Now, we can calculate the final answer by evaluating the expression.

Number of words with vowels not together = 6! - 5!
= 720 - 120
= 600

Therefore, the number of words formed from the letters of the word EAMCET such that two vowels are never together is 600.

Hence, the correct answer is option C) 600.