शब्द ‘DELHI’ के सभी अक्षरों का प्रयोग करते हुए कितने विभिन्न 5-अक्षरी शब्द (जिनका कोई अर्थ हो या न हो) बनाए जा सकते हैं, जबकि प्रत्येक शब्द D के साथ शुरू होता है और I के साथ समाप्त होता है?
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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
उत्तर और व्याख्या · explanation in English
Answer: (d) 6
With D fixed first and I fixed last, only E, L and H are left to arrange in the three middle places. Three distinct letters can be arranged in 3! = 6 ways.
- Positions 1 and 5 are fixed: D _ _ _ I.
- E, L and H fill the three middle places in 3! = 3 × 2 × 1 = 6 ways.
- Check: DELHI, DEHLI, DLEHI, DLHEI, DHELI, DHLEI — six words.
Remember · Fix the letters whose places are given, then arrange only the remaining ones: n distinct letters give n! orders.
Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·