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
How many different 5 letter words from DELHI ?
Solution:
1. Since D and I are fixed at the start and end positions, we only need to arrange the remaining three letters (E, L, H) in the middle positions.
2. Formula for arranging n distinct objects = n!
In this case, n = 3 (for letters E, L, H)
3. Calculation:
3! = 3 × 2 × 1 = 6
Therefore, there are 6 different possible arrangements.
Possible words:
– DELHI
– DEHLI
– DHELII
– DHELI
– DLHEI
– DLEHI