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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
3 black  4 white  5 red  Σ=12 balls  to take 3 balls there are C_3 ^(12) =220 ways  (a)  p=((3×4×5)/(220))=(3/(11))  (b)  2 red+1 other or 3 red only  p=((C_2 ^5 ×C_1 ^7 +C_3 ^5 )/(220))=(4/(11))  (c)  1 red+2 other or no red+ 3 other  p=((C_1 ^5 ×C_2 ^7 +C_3 ^7 )/(220))=(7/(11))
$$\mathrm{3}\:{black} \\ $$$$\mathrm{4}\:{white} \\ $$$$\mathrm{5}\:{red} \\ $$$$\Sigma=\mathrm{12}\:{balls} \\ $$$${to}\:{take}\:\mathrm{3}\:{balls}\:{there}\:{are}\:{C}_{\mathrm{3}} ^{\mathrm{12}} =\mathrm{220}\:{ways} \\ $$$$\left({a}\right) \\ $$$${p}=\frac{\mathrm{3}×\mathrm{4}×\mathrm{5}}{\mathrm{220}}=\frac{\mathrm{3}}{\mathrm{11}} \\ $$$$\left({b}\right) \\ $$$$\mathrm{2}\:{red}+\mathrm{1}\:{other}\:{or}\:\mathrm{3}\:{red}\:{only} \\ $$$${p}=\frac{{C}_{\mathrm{2}} ^{\mathrm{5}} ×{C}_{\mathrm{1}} ^{\mathrm{7}} +{C}_{\mathrm{3}} ^{\mathrm{5}} }{\mathrm{220}}=\frac{\mathrm{4}}{\mathrm{11}} \\ $$$$\left({c}\right) \\ $$$$\mathrm{1}\:{red}+\mathrm{2}\:{other}\:{or}\:{no}\:{red}+\:\mathrm{3}\:{other} \\ $$$${p}=\frac{{C}_{\mathrm{1}} ^{\mathrm{5}} ×{C}_{\mathrm{2}} ^{\mathrm{7}} +{C}_{\mathrm{3}} ^{\mathrm{7}} }{\mathrm{220}}=\frac{\mathrm{7}}{\mathrm{11}} \\ $$
Commented by Tawa11 last updated on 06/Sep/21
Great sir
$$\mathrm{Great}\:\mathrm{sir} \\ $$

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