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Permutation and CombinationQuestion and Answers: Page 1

Question Number 227529 Answers: 0 Comments: 0

There are cards in 30 different colors, with 70 cards of each color. Initially, 70 cards are selected and laid out in a stack from top to bottom. One operation consists of: choosing an X from the bottom 20 cards, such that its color has not appeared in the top 50 cards; then choosing a Y from the top 50 cards, such that its color has appeared at least twice in the top 50 cards; removing X and placing it right above Y. Repeat this process until no more valid X can be chosen. (1) Prove that the number of operations is finite. (2) For all possible initial configurations and sequences of operations, find the maximum possible number of operations.

$$ \\ $$There are cards in 30 different colors, with 70 cards of each color. Initially, 70 cards are selected and laid out in a stack from top to bottom. One operation consists of: choosing an X from the bottom 20 cards, such that its color has not appeared in the top 50 cards; then choosing a Y from the top 50 cards, such that its color has appeared at least twice in the top 50 cards; removing X and placing it right above Y. Repeat this process until no more valid X can be chosen. (1) Prove that the number of operations is finite. (2) For all possible initial configurations and sequences of operations, find the maximum possible number of operations.

Question Number 227151 Answers: 1 Comments: 0

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Question Number 227102 Answers: 1 Comments: 0

(m/n)

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Question Number 227098 Answers: 1 Comments: 0

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Question Number 226289 Answers: 0 Comments: 0

Question Number 226044 Answers: 1 Comments: 0

Question Number 224709 Answers: 1 Comments: 0

Question Number 224641 Answers: 1 Comments: 0

Question Number 224634 Answers: 1 Comments: 0

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Question Number 224623 Answers: 2 Comments: 2

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Question Number 224398 Answers: 0 Comments: 5

Question Number 224261 Answers: 0 Comments: 7

If I have 10 people and I want to create pairings, so that every person is matched with every other person at least once, how many unique pairings will there be in total?

Question Number 222192 Answers: 1 Comments: 0

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?

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

Question Number 222105 Answers: 1 Comments: 1