**Balls falling in buckets: "If X balls are dropped randomly into Y buckets..."**

Hello,

I have a question:

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**If X balls are dropped randomly into Y buckets (and buckets can hold an unlimited number of balls), what is the probability that n out of Y buckets are empty?**

Backstory: I schedule events. My boss has about 100 events a year and wants me to make sure that at least one is scheduled for every week. But it's very hard to pick particular dates for events (I have to coordinate across a lot of people's schedules). Last week my boss got mad because there were no events scheduled that week. I'd like to be able to show my boss that the probability of having at least one event every week across the whole year is low, so she realizes I'm doing my job as well as I can.

Backstory: I schedule events. My boss has about 100 events a year and wants me to make sure that at least one is scheduled for every week. But it's very hard to pick particular dates for events (I have to coordinate across a lot of people's schedules). Last week my boss got mad because there were no events scheduled that week. I'd like to be able to show my boss that the probability of having at least one event every week across the whole year is low, so she realizes I'm doing my job as well as I can.

Thank you!