How many different 5-letter words (with or without meaning) can be constructed using all the letters of the word ‘DELHI’ so that each word has to start with D and end with I?

The correct answer is 6 (Option 4).

Step-by-step Explanation:

We are asked to find the total number of 5-letter words (with or without meaning) that can be formed using all the letters of the word ‘DELHI’ such that:

1. The word starts with the letter 'D'.
2. The word ends with the letter 'I'.

Step 1: Analyze the given word

The word ‘DELHI’ consists of 5 distinct letters: D, E, L, H, I.

Step 2: Fix the positions of specified letters

Let the 5 positions in the word be represented as: [1st, 2nd, 3rd, 4th, 5th].

- 1st position: Must be filled by 'D'. There is only 1 choice.
- 5th position: Must be filled by 'I'. There is only 1 choice.

Step 3: Arrange the remaining letters

The remaining middle 3 positions (2nd, 3rd, and 4th) need to be filled using the remaining 3 letters: E, L, H.

The number of ways to arrange 3 distinct objects into 3 positions is given by 3 factorial (3!):

$3!=3\times 2\times 1=6$

Step 4: Calculate total arrangements

Total number of valid words = (Ways to choose 1st letter) × (Ways to choose middle 3 letters) × (Ways to choose 5th letter)

$\text{Total words}=1\times 6\times 1=6$

Therefore, exactly 6 such words can be constructed.