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Partition counting problem with cap on pairwise intersection

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#combinatorics #balls-in-bins #set-partition
165
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Bound the probability that the number of red balls in a random partition of a set of balls into 2 equal sized sets is close to the mean.

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#probability #balls-in-bins
776
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Application of Pigeon-Hole Principle to balls in bins.

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#combinatorics #pigeonhole-principle #balls-in-bins
145
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Probability of having K cigarettes in one of the 2 packs of cigarettes

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#probability #balls-in-bins
275
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Expected value of trials to obtain a red ball in a box of white balls.

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#probability #statistics #expectation #balls-in-bins
2.4k
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Number of solutions of $x_1+x_2+\dots+x_k=n$ with $x_i\le r$

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#combinatorics #inclusion-exclusion #balls-in-bins
1.2k
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Probability of events after a random ball was moved from one box to another

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#probability #combinatorics #balls-in-bins
840
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Total number of empty boxes

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#probability #balls-in-bins
1.8k
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Use the inclusion-exclusion principle to determine

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#combinatorics #inclusion-exclusion #balls-in-bins
19.1k
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Number of ways of distributing balls into boxes

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#combinatorics #balls-in-bins
1.6k
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Expected value of size of subset

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#probability #expectation #balls-in-bins
139
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coefficient on $s^{14}$ in generating function

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#generating-functions #balls-in-bins #multinomial-coefficients
68
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Find the number of unique paths, given a fixed set, that produce a given output.

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#probability #balls-in-bins
361
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Small o-notation in probability [Raab 1998 proof]

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#probability #asymptotics #balls-in-bins
89
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Balls and Bins when #balls < #bins

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#probability #asymptotics #balls-in-bins

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