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Is there a fast, reasonably accurate estimator for multinomial PDF?

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How many positive integer solutions are there to the equality $x_1+x_2+...+x_r= n$?

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Making 400k random choices from 400k samples seems to always end up with 63% distinct choices, why?

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#probability #random #balls-in-bins
2.1k
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Expected number of bins with more than one ball

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#probability #expectation #balls-in-bins
365
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Probability of drawing a run of a specific color from an urn with two colors of balls

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#probability #combinatorics #balls-in-bins
445
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Occupancy distribution bounds for $k$ balls in $m$ bins

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#probability-distributions #martingales #balls-in-bins #coupon-collector
376
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Distribution of maximum/minimum proportion in a sampling process

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#probability-distributions #stochastic-processes #balls-in-bins
1.2k
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Probability of assigning balls into buckets, where each bucket has a certain capacity.

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#probability #combinatorics #balls-in-bins
681
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If I randomly throw 10,000 balls to 4,000 buckets, what is the probability that at least one bucket contains more than 10 balls?

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#probability #balls-in-bins
377
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Probability that the first $2$ balls are white, given that the sample contains exactly $6$ white balls

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#probability #combinatorics #balls-in-bins
2.4k
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If five numbered balls are taken at random, find probability that the second largest number is 8

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851
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r distinct objects into n distinct boxes ( ordering of objects in each box matters)

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#combinatorics #discrete-mathematics #balls-in-bins
8.5k
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r identical objects into n distinct boxes

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#combinatorics #discrete-mathematics #balls-in-bins
169
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A Question on distribution numbers

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#combinatorics #permutations #balls-in-bins
158
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balls in bins -- waiting time until $k$ bins are occupied

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#probability #statistics #stochastic-processes #balls-in-bins #coupon-collector

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