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Question Number 13336 by tawa tawa last updated on 19/May/17
$$\mathrm{A}\:\mathrm{debating}\:\mathrm{team}\:\mathrm{is}\:\mathrm{to}\:\mathrm{be}\:\mathrm{selected}\:\mathrm{from}\:\mathrm{a}\:\mathrm{group}\:\mathrm{of}\:\mathrm{8}\:\mathrm{boys}\:\mathrm{and}\:\mathrm{6}\:\mathrm{girls}.\:, \\ $$$$\mathrm{in}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{this}\:\mathrm{be}\:\mathrm{done}\:\mathrm{if}\:\mathrm{the}\:\mathrm{team}\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Must}\:\mathrm{be}\:\mathrm{either}\:\mathrm{all}\:\mathrm{boys}\:\mathrm{or}\:\mathrm{all}\:\mathrm{girls} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Must}\:\mathrm{consist}\:\mathrm{of}\:\mathrm{two}\:\mathrm{boys}\:\mathrm{and}\:\mathrm{two}\:\mathrm{girls} \\ $$
Commented by tawa tawa last updated on 19/May/17
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}.\:\mathrm{i}\:\mathrm{understand}. \\ $$
Commented by mrW1 last updated on 19/May/17
$${to}\:\left({a}\right):\:{how}\:{many}\:{persons}\:{should}\:{be} \\ $$$${selected}? \\ $$$${If}\:\mathrm{4}\:{persons}\:{are}\:{to}\:{be}\:{selected},\:{then} \\ $$$$\left({a}\right)\:{C}_{\mathrm{4}} ^{\mathrm{8}} +{C}_{\mathrm{4}} ^{\mathrm{6}} =\mathrm{70}+\mathrm{15}=\mathrm{85}\:{ways} \\ $$
Answered by mrW1 last updated on 19/May/17
$$\left({b}\right) \\ $$$${C}_{\mathrm{2}} ^{\mathrm{8}} ×{C}_{\mathrm{2}} ^{\mathrm{6}} =\mathrm{28}×\mathrm{15}=\mathrm{420}\:{ways} \\ $$
Commented by tawa tawa last updated on 19/May/17
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$