What are the odds of a weekly event happening on a specific day X times out Y total weeks?

Question

Assuming there are no other variables and the event is 100% random, what are the odds of the following:

An event happens once, and only once, per week without exception. The day that the event happens is random and includes the possibility of happening two days in a row if the first is at the end of the week (i.e. Saturday) and the second is at the start of the next week (i.e. Sunday). What are both the odds and probability of the event happening on a specific day (e.g. Friday) exactly 17 times (or X) out of 52 weeks (or Y) in no particular order?

Answer 1

Each week there are 7 possible outcomes and presumably they are independent events.

Thus the probability of any day is 1/7.

Multiple weeks constitute binomial trials with p=1/7 and q=6/7 and the probability you seek is given by the binomial distribution.