Find the number of arrangements of the letters of the INDEPENDENCE. In how many of these arrangements,(i)         do the words start with P(ii)        do all the vowels always occur together(iii)       do the vowels never occur together(iv)       do the words begin with I and end in P?

Explanation

To solve the problem of finding the number of arrangements of the letters in the word "INDEPENDENCE" and answering the specific questions, we will follow these steps:

### Step 1: Calculate the total number of arrangements of the letters in "INDEPENDENCE".

The word "INDEPENDENCE" consists of 12 letters where:
- I appears 1 time
- N appears 3 times
- D appears 2 times
...