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Hi, i have a couple of problems that im not sure about (i get the wrong answer for particular cases because the probability add up to more than 1)

say you have 50 balls and 20 bins, you throw all 50 balls into the bins, with equal probability of a ball landing in each bin

1. what is the probability that at least one of the bins has more than 5 balls?

2. what's the probability at least 3 bins are empty?

are there any general formulas for b balls, n bins, more than x balls in at least one bin and at least y bins empty?

P.S this is the same problem as rolling a 20 sided dice 50 times i think, might help

say you have 50 balls and 20 bins, you throw all 50 balls into the bins, with equal probability of a ball landing in each bin

1. what is the probability that at least one of the bins has more than 5 balls?

2. what's the probability at least 3 bins are empty?

are there any general formulas for b balls, n bins, more than x balls in at least one bin and at least y bins empty?

P.S this is the same problem as rolling a 20 sided dice 50 times i think, might help

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