DELHI Word Letter Permutations

The problem asks for the total number of words, with or without meaning, that can be formed by using all the letters of the word "DELHI".

First, identify the word and count its letters. The word is "DELHI". It has 5 letters.

Next, check if all the letters are distinct. The letters in "DELHI" are D, E, L, H, I. All 5 letters are unique.

Calculating Word Arrangements

When all the letters in a word are distinct, the number of possible arrangements (permutations) is calculated using the factorial of the total number of letters. The formula for the number of permutations of $n$ distinct items is $n!$.

In this case, $n = 5$ (the number of letters in DELHI).

The calculation is as follows:

Number of words = $5!$

Where $5!$ (read as "5 factorial") means multiplying 5 by all the positive integers less than 5:

$5! = 5 \times 4 \times 3 \times 2 \times 1$

Calculating the product:

$5 \times 4 = 20$

$20 \times 3 = 60$

$60 \times 2 = 120$

$120 \times 1 = 120$

Therefore, there are 120 distinct words that can be formed using all the letters of the word "DELHI".