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Question Number 27270 by das47955@mail.com last updated on 05/Jan/18
$$\left(\mathrm{1}\right)\:\boldsymbol{\mathrm{There}}\:\boldsymbol{\mathrm{are}}\:\mathrm{20}\:\boldsymbol{\mathrm{boys}}\:\boldsymbol{\mathrm{and}}\:\mathrm{10}\:\boldsymbol{\mathrm{girls}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{a}} \\ $$$$\boldsymbol{\mathrm{class}}.\boldsymbol{\mathrm{If}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{committee}}\:\boldsymbol{\mathrm{of}}\:\mathrm{6}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{be}} \\ $$$$\boldsymbol{\mathrm{chosen}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{random}}\:\boldsymbol{\mathrm{having}}\:\boldsymbol{\mathrm{atleast}} \\ $$$$\mathrm{2}\:\boldsymbol{\mathrm{boys}}\:\boldsymbol{\mathrm{and}}\:\mathrm{2}\:\boldsymbol{\mathrm{girls}},\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\: \\ $$$$\boldsymbol{\mathrm{probability}}\:\boldsymbol{\mathrm{that}} \\ $$$$\left(\boldsymbol{\mathrm{i}}\right)\:\boldsymbol{\mathrm{there}}\:\boldsymbol{\mathrm{ara}}\:\mathrm{3}\:\boldsymbol{\mathrm{boys}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{the}}\: \\ $$$$\boldsymbol{\mathrm{committee}} \\ $$$$\left(\boldsymbol{\mathrm{ii}}\right)\:\boldsymbol{\mathrm{there}}\:\boldsymbol{\mathrm{are}}\:\mathrm{4}\:\boldsymbol{\mathrm{boys}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{the}}\: \\ $$$$\boldsymbol{\mathrm{committee}} \\ $$