Find the number of permutations that can be made from the letters of the word 'OMEGA'. E being always in the middle.

Options

A. a. 18 ways
B. b. 24 ways
C. c. 48 ways
D. d. 20 ways

Answer

To find the number of permutations that can be made from the letters of the word "OMEGA" with the letter 'E' always in the middle, we can follow these steps:

### Step 1: Fix the position of 'E'
Since 'E' must always be in the middle, we can fix it in the third position of the arrangement. The arrangement looks like this:

```
_ _ E _
```

### Step 2: Identify the remaining letters
The remaining letters we have to arrange are O, M, G, and A. So, we have 4 letters left to arrange.

### Step 3: Calculate the number of permutations of the remaining letters
The number of ways to arrange n distinct objects is given by n!. In our case, we have 4 distinct letters (O, M, G, A). Thus, the number of permutations of these 4 letters is:

\[ 4! = 4 \times 3 \times 2 \times 1 = 24 \]

### Step 4: Conclusion
Therefore, the total number of permutations of the letters of the word "OMEGA" with 'E' always in the middle is **24**.

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