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Invariance of residues modulo $p$

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#elementary-number-theory #prime-numbers #permutations #reduced-residue-system
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couple wedding seating problem

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#permutations
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K Permutations, 7 letter string, alphabet, no repeats

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#combinatorics #permutations
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Choose 2 numbers from 100 numbers

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#combinatorics #permutations #combinations
128
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How many different rectangles of maximum horizontal side K can be formed in an N x N grid?

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#combinatorics #permutations #least-squares #rectangles
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Number of ways to arrange 3 boys and 5 girls in line if the boys must stand next to each other?

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#permutations #combinations
117
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Ways to arrange couples

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#combinatorics #permutations
77
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Random permutation of cards where each player knows only his cards

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#permutations #random
500
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Transitive subgroups of $S_n$

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#group-theory #finite-groups #permutations #symmetric-groups
460
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Suppose 6 people are queueing for a bus. If all orderings are equally likely, what is probability that Jack is in front of Jill?

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#probability #permutations #combinations
1.9k
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Could you please solve this problem?

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#permutations #combinations
49
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How many possible ways to cross the bridges at once, if we know the problem has solution?

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#combinatorics #permutations #combinations
398
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Lottery exam question

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#combinatorics #permutations #computer-science #combinations
85
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Prove that $(^nC_0)^2 + (^nC_1)^2 + (^nC_2)^2 + \cdots + (^nC_n)^2 = {^{2n}C}_n$

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#permutations #combinations
396
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Difference between cycle composition and cycle product

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#abstract-algebra #permutations

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