# Q. 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?

(a) 24

(b) 18

(c) 12

(d) 6

Correct Answer: (d) 6

#### Question from UPSC Prelims 2020 CSAT Paper

**Explanation :**

## Different words formed from DELHI

The number of different 5-letter words that can be constructed using all the letters of the word ‘DELHI’ so that each word has to start with D and end with I is 6.

Since the first and last letters are fixed as D and I respectively, we only need to arrange the remaining three letters (E, L and H) in between. The number of ways to arrange n distinct objects is given by n!, where n is the number of objects. In this case, we have 3 distinct letters to arrange so there are 3! = 3 × 2 × 1 = 6 different ways to arrange them.

Therefore, there are a total of 6 different 5-letter words that can be constructed using all the letters of the word ‘DELHI’ so that each word has to start with D and end with I.