In how many ways can letters of the word PENCIL , be arranged so that E and N are always together.
शब्द PENCIL के अक्षरों को कितने तरीकों से व्यवस्थित किया जा सकता है ताकि E और N हमेशा एक साथ रहें।

Options

A. 240
B. 120
C. 260
D. 720

Answer

To solve the problem of arranging the letters of the word "PENCIL" such that the letters E and N are always together, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Letters**: The word "PENCIL" consists of 6 letters: P, E, N, C, I, L.

2. **Group E and N Together**: Since E and N must always be together, we can treat them as a single unit or block. Thus, we can represent the block as (EN) or (NE).

3. **Count the Total Units**: After grouping E and N together, we now have the following units to arrange:
- (EN) or (NE)
- P
- C
- I
- L
This gives us a total of 5 units: (EN), P, C, I, L.

4. **Calculate Arrangements of the Units**: The number of ways to arrange these 5 units is given by the factorial of the number of units:
\[ 5! = 120 \]

5. **Account for the Arrangement of E and N**: Since E and N can be arranged in two ways within their block (either EN or NE), we need to multiply the arrangements of the units by 2:
\[ \text{Total arrangements} = 2 \times 5! = 2 \times 120 = 240 \]

### Final Answer:
The total number of ways to arrange the letters of the word "PENCIL" such that E and N are always together is **240**.

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