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Category: Permutation and Combination

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 $${there}\:{are}\:\mathrm{32}\:{students}\:{in}\:{a}\:{class}.\:{for} \\ $$$${each}\:{competition}\:{in}\:{a}\:{sport}\:{event}\: \\ $$$${in}\:{the}\:{school}\:{each}\:{class}\:{can}\:{send} \\ $$$${a}\:{team}\:{with}\:{three}\:{students}.\:{if}\:{no} \\ $$$${two}\:{students}\:{may}\:{be}\:{in}\:{the}\:{same} \\ $$$${team}\:{for}\:{more}\:{than}\:{one}\:{time},\:{in} \\ $$$${how}\:{many}\:{different}\:{competitions}\: \\ $$$${can}\:{this}\:{class}\:{participate}?…