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?

Correct Option (D)

The word 'DELHI' comprises five distinct letters: D, E, L, H, I. The problem specifies the formation of 5-letter words with two conditions:

• The word must commence with the letter 'D'.
• The word must conclude with the letter 'I'.

Given these constraints:

• The first position of the 5-letter word is fixed by 'D'.
• The fifth position of the 5-letter word is fixed by 'I'.
• This leaves the letters E, L, and H to be arranged in the three intermediate positions (second, third, and fourth).
• Since these three letters are distinct and are to be arranged in three distinct positions, the number of possible arrangements is given by 3! (3 factorial).
• Calculation: 3! = 3 × 2 × 1 = 6.

Therefore, 6 different 5-letter words can be constructed under the stipulated conditions.

Incorrect Options:

Options A (24), B (18), and C (12) are incorrect. These values do not correspond to the correct application of permutation principles under the given constraints. The calculation must specifically account for the fixed positions of 'D' and 'I', which reduces the number of letters available for arrangement to three and the number of positions for arrangement to three, resulting in 3! permutations.