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A committee of 5 members is to be formed from 8 men and 6 women, with at least 3 women. Which expression represents the number of such committees?8 पुरुषों और 6 महिलाओं में से 5 सदस्यों की समिति बनानी है, जिसमें कम-से-कम 3 महिलाएँ हों। ऐसी समितियों की संख्या को कौन-सा व्यंजक दर्शाता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\binom{6}{3}\binom{8}{2}+\binom{6}{4}\binom{8}{1}+\binom{6}{5}\binom{8}{0}\)\(\binom{6}{3}\binom{8}{2}+\binom{6}{4}\binom{8}{1}+\binom{6}{5}\binom{8}{0}\)
With at least 3 women, the possible cases are 3, 4, or 5 women. They require 2, 1, or 0 men respectively, so all three product terms are added. Exam tip: check that each case totals the committee size of 5.कम-से-कम 3 महिलाओं के मामले 3, 4 या 5 महिलाएँ हैं। इनके साथ क्रमशः 2, 1 या 0 पुरुष चुने जाते हैं, इसलिए तीनों गुणन पद जोड़े जाते हैं। परीक्षा में शेष सदस्य हमेशा कुल समिति आकार से जाँचें।
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