Question Number 158995 by Raxreedoroid last updated on 11/Nov/21
A population of 15 items. 4 red, 6 black and 5 green. a sample of 4 items are selected. what is the probability that the sample contains 3 black and 1 green?
Commented by tounghoungko last updated on 14/Nov/21
$${p}=\frac{{C}_{\mathrm{3}} ^{\mathrm{6}} ×{C}_{\mathrm{1}} ^{\mathrm{5}} }{{C}_{\mathrm{4}} ^{\mathrm{15}} }\:=\:\frac{\mathrm{20}×\cancel{\mathrm{5}}}{\frac{\cancel{\mathrm{15}}\:^{\mathrm{3}} ×\cancel{\mathrm{14}}\:^{\mathrm{7}} ×\mathrm{13}×\cancel{\mathrm{12}}}{\cancel{\mathrm{4}×\mathrm{3}}×\cancel{\mathrm{2}×\mathrm{1}}}}\: \\ $$$${p}=\:\frac{\mathrm{20}}{\mathrm{21}×\mathrm{13}} \\ $$