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Question Number 174855 by byaw last updated on 12/Aug/22

$$\mathrm{Find}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{ways}$$$$\mathrm{a}\mathrm{committee}\mathrm{of}4\mathrm{people}\mathrm{can}\mathrm{be}$$$$\mathrm{chosen}\mathrm{from}\mathrm{a}\mathrm{group}\mathrm{of}5\mathrm{men}$$$$\mathrm{and}7\mathrm{women}\mathrm{when}\mathrm{it}\mathrm{contains}$$$$\mathrm{people}\mathrm{of}\mathrm{both}\mathrm{sexes}\mathrm{and}$$$$\mathrm{there}\mathrm{are}\mathrm{at}\mathrm{least}\mathrm{as}\mathrm{many}$$$$\mathrm{women}\mathrm{as}\mathrm{men}.$$

Answered by Kallu last updated on 12/Aug/22

$$$$$$case1:2menand2women$$$$no.ofways={}^{5_{C_2}}\times {}^{7_{C_2}}=210$$$$$$$$case2:1manand3women$$$$no.ofways={}^{5_{C_1}}\times {}^{7_{C_3}}=175$$$$$$$$Thereforetotalways=385$$$$$$

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