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there-are-32-students-in-a-class-for-each-competition-in-a-sport-event-in-the-school-each-class-can-send-a-team-with-three-students-if-no-two-students-may-be-in-the-same-team-for-more-than-one-time




Question Number 222192 by mr W last updated on 22/Jun/25
there are 32 students in a class. for  each competition in a sport event   in the school each class can send  a team with three students. if no  two students may be in the same  team for more than one time, in  how many different competitions   can this class participate?
$${there}\:{are}\:\mathrm{32}\:{students}\:{in}\:{a}\:{class}.\:{for} \\ $$$${each}\:{competition}\:{in}\:{a}\:{sport}\:{event}\: \\ $$$${in}\:{the}\:{school}\:{each}\:{class}\:{can}\:{send} \\ $$$${a}\:{team}\:{with}\:{three}\:{students}.\:{if}\:{no} \\ $$$${two}\:{students}\:{may}\:{be}\:{in}\:{the}\:{same} \\ $$$${team}\:{for}\:{more}\:{than}\:{one}\:{time},\:{in} \\ $$$${how}\:{many}\:{different}\:{competitions}\: \\ $$$${can}\:{this}\:{class}\:{participate}? \\ $$
Answered by vnm last updated on 22/Jun/25
I think the answer is 32×5=160  I can′t save images in this program, I don′t know why,   so I′ve saved picture here:  https://ibb.co/4RpVVWcZ  points are students, triangles are teams.  all the segments have different sizes.
$$\mathrm{I}\:\mathrm{think}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{is}\:\mathrm{32}×\mathrm{5}=\mathrm{160} \\ $$$$\mathrm{I}\:\mathrm{can}'\mathrm{t}\:\mathrm{save}\:\mathrm{images}\:\mathrm{in}\:\mathrm{this}\:\mathrm{program},\:\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}\:\mathrm{why},\: \\ $$$$\mathrm{so}\:\mathrm{I}'\mathrm{ve}\:\mathrm{saved}\:\mathrm{picture}\:\mathrm{here}: \\ $$$$\mathrm{https}://\mathrm{ibb}.\mathrm{co}/\mathrm{4RpVVWcZ} \\ $$$$\mathrm{points}\:\mathrm{are}\:\mathrm{students},\:\mathrm{triangles}\:\mathrm{are}\:\mathrm{teams}. \\ $$$$\mathrm{all}\:\mathrm{the}\:\mathrm{segments}\:\mathrm{have}\:\mathrm{different}\:\mathrm{sizes}. \\ $$
Commented by mr W last updated on 22/Jun/25
thanks sir!  actually i don′t have the answer. i′ll  study your solution.  this is your image you can′t post:
$${thanks}\:{sir}! \\ $$$${actually}\:{i}\:{don}'{t}\:{have}\:{the}\:{answer}.\:{i}'{ll} \\ $$$${study}\:{your}\:{solution}. \\ $$$${this}\:{is}\:{your}\:{image}\:{you}\:{can}'{t}\:{post}: \\ $$
Commented by mr W last updated on 22/Jun/25

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