A set of 60 different days is selected from a given year. Assume that all sets of cardinality 60 are equally likely. Also, for simplicity, assume that the year has only 360 days, divided into twelve 30-day months. Evaluate the probabilities of the following events.

Question

A set of 60 different days is selected from a given year. Assume that all sets of cardinality 60 are equally likely. Also, for simplicity, assume that the year has only 360 days, divided into twelve 30-day months. Evaluate the probabilities of the following events.
1.Exactly 5 days are selected from each of the 12 months.
2.None of the selected days is from January.
3.There exist 3 different months such that exactly 20 days are selected from each one of these months.