Find the number of words formed by permuting all letters of the word INDIA. In how many of them vowels are together ?

Explanation

To solve the problem of finding the number of words formed by permuting all letters of the word "INDIA" and how many of them have the vowels together, we can follow these steps:

### Step 1: Calculate the total number of permutations of the letters in "INDIA".

The word "INDIA" consists of 5 letters, where the letter 'I' appears twice. The formula for the number of permutations of letters when there are repetitions is given by:

\[
\text{Total permutations} = \frac{n!}{p_1! \times p_2! \times \ldots \times p_k!}
...