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In a row of (7) distinct objects, the relative order of (A), (B), (C) must be (A) then (B) then (C). How many arrangements are possible?(7) अलग-अलग वस्तुओं की पंक्ति में (A), (B), (C) का सापेक्ष क्रम (A) फिर (B) फिर (C) होना चाहिए। कितनी व्यवस्थाएं होंगी?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (840)(840)
Among total (7!) arrangements, the (3!) relative orders of (A,B,C) are equally likely, so (\frac{7!}{3!}) are valid. Exam tip: divide by factorial for fixed relative order.कुल (7!) व्यवस्थाओं में (A,B,C) के (3!) सापेक्ष क्रम समान हैं, इसलिए (\frac{7!}{3!}) मान्य हैं। परीक्षा में fixed relative order के लिए factorial से divide करें।
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