Step 1: Understanding the Question:
We need to find the number of arrangements of the letters of the word "COCHIN" such that the two 'C's are never separated (meaning they must always remain adjacent).
Step 2: Key Formula or Approach:
We use the bundling/string method:
1. Treat the group of letters that must stay together as a single block.
2. Find the number of permutations of this block along with the remaining individual letters.
3. Multiply by the number of arrangements of the letters inside the block itself.
Step 3: Detailed Explanation:
1. The word "COCHIN" has 6 letters: C, O, C, H, I, N (where 'C' is repeated twice).
2. Since the two 'C's must never be separated, we group them together into a single block: \(\text{[CC]}\).
3. We now treat this block as a single item. The set of items to arrange is:
- The block \(\text{[CC]}\) (1 item)
- The letter O (1 item)
- The letter H (1 item)
- The letter I (1 item)
- The letter N (1 item)
4. This gives a total of 5 distinct items to arrange.
5. The number of linear arrangements of these 5 items is:
\[ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \text{ ways} \]
6. Within the block \(\text{[CC]}\), both letters are identical, so swapping their positions does not create a new unique word (\(\frac{2!}{2!} = 1\) arrangement).
7. Therefore, the total number of permutations is:
\[ 120 \times 1 = 120 \text{ arrangements} \]
This matches Option (B).
Step 4: Final Answer:
The number of ways to arrange the letters is \(120\), which corresponds to Option (B).