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# Question-142253

Question Number 142253 by mathdave last updated on 28/May/21
Answered by mr W last updated on 28/May/21
$$\mathrm{3}\:{black} \\$$$$\mathrm{4}\:{white} \\$$$$\mathrm{5}\:{red} \\$$$$\Sigma=\mathrm{12}\:{balls} \\$$$${to}\:{take}\:\mathrm{3}\:{balls}\:{there}\:{are}\:{C}_{\mathrm{3}} ^{\mathrm{12}} =\mathrm{220}\:{ways} \\$$$$\left({a}\right) \\$$$${p}=\frac{\mathrm{3}×\mathrm{4}×\mathrm{5}}{\mathrm{220}}=\frac{\mathrm{3}}{\mathrm{11}} \\$$$$\left({b}\right) \\$$$$\mathrm{2}\:{red}+\mathrm{1}\:{other}\:{or}\:\mathrm{3}\:{red}\:{only} \\$$$${p}=\frac{{C}_{\mathrm{2}} ^{\mathrm{5}} ×{C}_{\mathrm{1}} ^{\mathrm{7}} +{C}_{\mathrm{3}} ^{\mathrm{5}} }{\mathrm{220}}=\frac{\mathrm{4}}{\mathrm{11}} \\$$$$\left({c}\right) \\$$$$\mathrm{1}\:{red}+\mathrm{2}\:{other}\:{or}\:{no}\:{red}+\:\mathrm{3}\:{other} \\$$$${p}=\frac{{C}_{\mathrm{1}} ^{\mathrm{5}} ×{C}_{\mathrm{2}} ^{\mathrm{7}} +{C}_{\mathrm{3}} ^{\mathrm{7}} }{\mathrm{220}}=\frac{\mathrm{7}}{\mathrm{11}} \\$$
Commented by Tawa11 last updated on 06/Sep/21
$$\mathrm{Great}\:\mathrm{sir} \\$$