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In a row arrangement of (8) distinct objects, exactly (3) objects must lie between two particular objects. How many arrangements are possible?(8) अलग-अलग वस्तुओं की पंक्ति व्यवस्था में दो विशेष वस्तुओं के बीच ठीक (3) वस्तुएं हों। कितनी व्यवस्थाएं होंगी?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (2880)(2880)
The two particular objects must have positions differing by (4), giving (4) position-pairs and (2!) orders. The remaining objects arrange in (6!) ways, so the total is (4\cdot2!\cdot6!=5760).दो विशेष वस्तुओं के स्थानों में (4) का अंतर होना चाहिए, ऐसे (4) position-pairs हैं और order (2!) है। बाकी (6!) तरीकों से सजेंगे, कुल (4\cdot2!\cdot6!=5760) है।
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