How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?

Explanation

To solve the problem of how many words can be formed using all the letters of the word "EQUATION" such that the vowels and consonants occur together, we can follow these steps:

### Step 1: Identify the Vowels and Consonants
The word "EQUATION" consists of the following letters:
- Vowels: E, U, A, I, O (Total: 5 vowels)
- Consonants: Q, T, N (Total: 3 consonants)

### Step 2: Treat Vowels and Consonants as Groups
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