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Question Number 35640 by NECx last updated on 21/May/18
$${A}\:{panel}\:{of}\:\mathrm{3}\:{women}\:{and}\:\mathrm{4}\:{men}\:{is} \\ $$$${to}\:{be}\:{formed}\:{from}\:\mathrm{8}\:{women}\:{and} \\ $$$$\mathrm{7}\:{men}.{Find}\:{the}\:{number}\:{of}\:{ways} \\ $$$${which}\:{the}\:{panel}\:{can}\:{be}\:{formed}\:{if} \\ $$$${it}\:{must}\:{contain}\:{at}\:{least}\:\mathrm{2}\:{women}. \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 21/May/18
$${W}=\mathrm{8}\:{M}=\mathrm{7}\:\:{panel}\left({W}\mathrm{3}+{M}\mathrm{4}\right) \\ $$$$\:\:\:{C}_{\mathrm{3}} ^{\mathrm{8}} ×{C}_{\mathrm{4}} ^{\mathrm{7}} \\ $$$${in}\:{first}\:{sentence}\:{it}\:{is}\:{said}\:{that}\:{psnel}\left({W}\mathrm{3}+{M}\mathrm{4}\right. \\ $$$${in}\:{last}\:{sentence}\:{panel}\:{contain}\:{atleast}\:\mathrm{2}{W} \\ $$$${so}\:{when}\:{number}\:{of}\:{woman}\:{in}\:{panelis}\:{fixed}\:\mathrm{3}\: \\ $$$${then}\:{how}\:{the}\:{term}\:{atlesst}\:{appear}\:{in}\:{question} \\ $$$${pls}\:{check}.... \\ $$$${if}\:{so}\:{then} \\ $$$${C}_{\mathrm{2}} ^{\mathrm{8}} ×{C}_{\mathrm{4}} ^{\mathrm{7}} \:+{C}_{\mathrm{3}} ^{\mathrm{8}} ×{C}_{\mathrm{4}} ^{\mathrm{7}} \\ $$$$ \\ $$