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A committee of (6) members is to be formed from (15) members. One fixed member must be included and two special members must not be included together. How many committees are possible?(15) सदस्यों में से (6) सदस्यों की समिति बनानी है। एक निश्चित सदस्य अवश्य शामिल हो और दो विशेष सदस्य साथ-साथ शामिल न हों, तो कितनी समितियां बनेंगी?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (1782)(1782)
After fixing the required member, choose (5) from the remaining (14) and subtract cases where both special members are together, (^{12}C_{3}). The answer is (^{14}C_{5}-{}^{12}C_{3}=1782).निश्चित सदस्य को शामिल मानकर शेष (14) में से (5) चुनें और दोनों विशेष साथ वाले (^{12}C_{3}) घटाएं। उत्तर (^{14}C_{5}-{}^{12}C_{3}=1782) है।
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