In how may ways can the letters of the word 'PENCIL' be arranged so that N is always next to E?

Explanation

To solve the problem of arranging the letters of the word "PENCIL" such that N is always next to E, we can follow these steps:

### Step-by-Step Solution:

1. **Group N and E Together**: Since N must always be next to E, we can treat the combination "NE" as a single unit or block. This reduces our problem to arranging the blocks.

2. **Identify the Blocks**: The letters in "PENCIL" are P, E, N, C, I, L. By grouping N and E together, we now have the following blocks to arrange: "NE", P, C, I, L. This gives us a total of 5 blocks: NE, P, C, I, L.

3. **Calculate the Arrangements of the Blocks**: The number of ways to arrange these 5 blocks is calculated using the factorial of the number of blocks. Therefore, the number of arrangements is:
\[ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \]

4. **Consider the Order of N and E**: Since N and E can be arranged in two ways (NE or EN), we need to multiply the number of arrangements of the blocks by the number of arrangements of N and E within their block:
\[ 120 \times 2 = 240 \]

5. **Final Answer**: Thus, the total number of ways to arrange the letters of the word "PENCIL" such that N is always next to E is 240.

### Final Result:
The letters of the word "PENCIL" can be arranged in **240 ways** such that N is always next to E.