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From (8) men and (7) women, a committee of (6) members is to be formed. The committee must have at most (3) women. How many committees are possible?(8) पुरुषों और (7) महिलाओं में से (6) सदस्यों की समिति बनानी है। समिति में महिलाओं की संख्या अधिकतम (3) होनी चाहिए। कुल कितनी समितियाँ बनेंगी?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (3850)(3850)
Subtract the cases with (4,5,6) women from total (\binom{15}{6}). For at most conditions, complement counting is often simpler.कुल (\binom{15}{6}) समितियों से (4,5,6) महिलाओं वाले मामले घटाएँ। अधिकतम वाली शर्त में पूरक गिनती आसान होती है।
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