In how many ways can 5 letter words be formed from `2^("nd"),5^("th"),6^("th"),8^("th")and9^("th")`letter of the word METICULOUS?

Options

A. 120
B. 60
C. 240
D. 24

Answer

To solve the problem of forming 5-letter words from the specified letters of the word "METICULOUS", we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Letters**:
We need to extract the letters from the positions specified in the question. The letters in the word "METICULOUS" are:
- 2nd letter: E
- 5th letter: C
- 6th letter: I
- 8th letter: O
- 9th letter: U

So, the letters we will use are: E, C, I, O, U.

2. **Count the Letters**:
We have a total of 5 letters: E, C, I, O, U. All these letters are unique.

3. **Calculate the Number of Arrangements**:
Since all the letters are unique, the number of ways to arrange these 5 letters can be calculated using the factorial of the number of letters. The formula for the number of arrangements of n unique letters is n!.

Here, n = 5, so we calculate:
\[ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \]

4. **Final Answer**:
The total number of ways to form 5-letter words from the letters E, C, I, O, U is 120.

### Summary:
The number of ways to form 5-letter words from the letters E, C, I, O, U is **120**.

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