Question and Answers Forum

All Questions      Topic List

Permutation and Combination Questions

Previous in All Question      Next in All Question      

Previous in Permutation and Combination      Next in Permutation and Combination      

Question Number 102800 by bramlex last updated on 11/Jul/20

There are 14 boys and 10 girls in  a classroom. The teacher wants  to form a team of 5 students .  The team must have a least two  boys and two girls . Find the  number of ways the team can be  chosen.

$$\mathrm{There}\:\mathrm{are}\:\mathrm{14}\:\mathrm{boys}\:\mathrm{and}\:\mathrm{10}\:\mathrm{girls}\:\mathrm{in} \\ $$$$\mathrm{a}\:\mathrm{classroom}.\:\mathrm{The}\:\mathrm{teacher}\:\mathrm{wants} \\ $$$$\mathrm{to}\:\mathrm{form}\:\mathrm{a}\:\mathrm{team}\:\mathrm{of}\:\mathrm{5}\:\mathrm{students}\:. \\ $$$$\mathrm{The}\:\mathrm{team}\:\mathrm{must}\:\mathrm{have}\:\mathrm{a}\:\mathrm{least}\:\mathrm{two} \\ $$$$\mathrm{boys}\:\mathrm{and}\:\mathrm{two}\:\mathrm{girls}\:.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{the}\:\mathrm{team}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{chosen}.\: \\ $$

Answered by bemath last updated on 11/Jul/20

case(1) 3boys &2 girls⇒C_3 ^(14)  ×C_2 ^(10)   =((14.13.12)/(3.2.1)) × ((10.9)/(2.1)) = 13680  (2)2boys &3 girls⇒C_2 ^(14) ×C_3 ^(10)  = ((14.13)/(2.1))×((10.9.8)/(3.2.1))  = 10920  totally = 13680+10920 =24600

$${case}\left(\mathrm{1}\right)\:\mathrm{3}{boys}\:\&\mathrm{2}\:{girls}\Rightarrow{C}_{\mathrm{3}} ^{\mathrm{14}} \:×{C}_{\mathrm{2}} ^{\mathrm{10}} \\ $$$$=\frac{\mathrm{14}.\mathrm{13}.\mathrm{12}}{\mathrm{3}.\mathrm{2}.\mathrm{1}}\:×\:\frac{\mathrm{10}.\mathrm{9}}{\mathrm{2}.\mathrm{1}}\:=\:\mathrm{13680} \\ $$$$\left(\mathrm{2}\right)\mathrm{2}{boys}\:\&\mathrm{3}\:{girls}\Rightarrow{C}_{\mathrm{2}} ^{\mathrm{14}} ×{C}_{\mathrm{3}} ^{\mathrm{10}} \:=\:\frac{\mathrm{14}.\mathrm{13}}{\mathrm{2}.\mathrm{1}}×\frac{\mathrm{10}.\mathrm{9}.\mathrm{8}}{\mathrm{3}.\mathrm{2}.\mathrm{1}} \\ $$$$=\:\mathrm{10920} \\ $$$${totally}\:=\:\mathrm{13680}+\mathrm{10920}\:=\mathrm{24600} \\ $$$$ \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com