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There-are-6-girls-and-four-boys-in-a-class-3-students-are-choosen-at-random-so-as-to-be-awarded-a-scholaship-In-how-many-ways-can-this-be-done-if-atlease-1-boy-and-1-girl-must-in-the-selection-




Question Number 75180 by Rio Michael last updated on 08/Dec/19
There are 6 girls and four boys in a class.  3 students are choosen at random so as to be  awarded a scholaship.In how many ways can  this be done if atlease 1 boy and 1 girl must  in the selection
$${There}\:{are}\:\mathrm{6}\:{girls}\:{and}\:{four}\:{boys}\:{in}\:{a}\:{class}. \\ $$$$\mathrm{3}\:{students}\:{are}\:{choosen}\:{at}\:{random}\:{so}\:{as}\:{to}\:{be} \\ $$$${awarded}\:{a}\:{scholaship}.{In}\:{how}\:{many}\:{ways}\:{can} \\ $$$${this}\:{be}\:{done}\:{if}\:{atlease}\:\mathrm{1}\:{boy}\:{and}\:\mathrm{1}\:{girl}\:{must} \\ $$$${in}\:{the}\:{selection} \\ $$$$ \\ $$
Commented by mr W last updated on 08/Dec/19
C_2 ^6 C_1 ^4 +C_2 ^4 C_1 ^6 =15×4+6×6=96  or  C_3 ^(10) −C_3 ^6 −C_3 ^4 =120−20−4=96
$${C}_{\mathrm{2}} ^{\mathrm{6}} {C}_{\mathrm{1}} ^{\mathrm{4}} +{C}_{\mathrm{2}} ^{\mathrm{4}} {C}_{\mathrm{1}} ^{\mathrm{6}} =\mathrm{15}×\mathrm{4}+\mathrm{6}×\mathrm{6}=\mathrm{96} \\ $$$${or} \\ $$$${C}_{\mathrm{3}} ^{\mathrm{10}} −{C}_{\mathrm{3}} ^{\mathrm{6}} −{C}_{\mathrm{3}} ^{\mathrm{4}} =\mathrm{120}−\mathrm{20}−\mathrm{4}=\mathrm{96} \\ $$
Commented by Rio Michael last updated on 08/Dec/19
thanks sir  i prefer method 1
$${thanks}\:{sir} \\ $$$${i}\:{prefer}\:{method}\:\mathrm{1} \\ $$

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