In how many ways can the letter of the word 'INSURANCE' be arranged, so that the vowels are never separate?

Explanation

To solve the problem of arranging the letters of the word "INSURANCE" such that the vowels are never separated, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Letters**:
The word "INSURANCE" consists of 9 letters in total: I, N, S, U, R, A, N, C, E.

2. **Identify the Vowels and Consonants**:
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