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Question Number 45920 by byaw last updated on 18/Oct/18

Answered by math1967 last updated on 19/Oct/18

i) All 4 balls are black= ((^8 c_2 )/(^(20) c_2 ))∩((^(15) c_2 )/(^(25) c_2 )) =((14)/(95))×(7/(20))=((49)/(950)) ans. ii) ((^(12) c_1 ×^8 c_1 )/(^(20) c_2 )) ×((^(15) c_2 )/(^(25) c_2 )) ∪((^(10) c_(1 ) ×^(15) c_1 )/(^(25) c_2 ))×((^8 c_2 )/(^(20) c_2 )) =((12×8×15×7)/(10×19×25×12)) +((10×15×4×7)/(25×12×10×19))

$$\left.{i}\right)\:{All}\:\mathrm{4}\:{balls}\:{are}\:{black}=\:\frac{\:^{\mathrm{8}} {c}_{\mathrm{2}} \:}{\:^{\mathrm{20}} {c}_{\mathrm{2}} }\cap\frac{\:^{\mathrm{15}} {c}_{\mathrm{2}} }{\:^{\mathrm{25}} {c}_{\mathrm{2}} }\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{14}}{\mathrm{95}}×\frac{\mathrm{7}}{\mathrm{20}}=\frac{\mathrm{49}}{\mathrm{950}}\:{ans}.\: \\ $$$$\left.{ii}\right)\:\frac{\:^{\mathrm{12}} {c}_{\mathrm{1}} ×\:^{\mathrm{8}} {c}_{\mathrm{1}} }{\:^{\mathrm{20}} {c}_{\mathrm{2}} }\:×\frac{\:^{\mathrm{15}} {c}_{\mathrm{2}} }{\:^{\mathrm{25}} {c}_{\mathrm{2}} }\:\cup\frac{\:^{\mathrm{10}} {c}_{\mathrm{1}\:} ×\:^{\mathrm{15}} {c}_{\mathrm{1}} }{\:^{\mathrm{25}} {c}_{\mathrm{2}} }×\frac{\:^{\mathrm{8}} {c}_{\mathrm{2}} }{\:^{\mathrm{20}} {c}_{\mathrm{2}} } \\ $$$$=\frac{\mathrm{12}×\mathrm{8}×\mathrm{15}×\mathrm{7}}{\mathrm{10}×\mathrm{19}×\mathrm{25}×\mathrm{12}}\:+\frac{\mathrm{10}×\mathrm{15}×\mathrm{4}×\mathrm{7}}{\mathrm{25}×\mathrm{12}×\mathrm{10}×\mathrm{19}} \\ $$$$ \\ $$

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