(i) How many words can be formed with the letters of the word, 'HARYANA'?
How many of these
(ii) have H and N together?
(iii) begin with H and end with N?
(iv) have 3 vowels together?

Explanation

To solve the problem, we will break it down into parts as per the questions asked.

### Given:
The word is "HARYANA", which consists of 7 letters: H, A, R, Y, A, N, A.

### Step 1: Count the total number of letters and their frequencies.
- Total letters = 7
- Frequencies:
...