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 probability 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 probability of the following events.
1)  Exactly 5 days are selected from each of the 12 months.
    a) (30 C 5)^2 / 360 C 60
    b) (30 C 5) / 360 C 60
    c) 30^12 / 360^60
    d) 360 / (30 C 5)^12 
2) None of the selected days is from January.
    a) 1 - (30 C 12)/ (360 C 60)
    b) 1 - (330 C 60)/(360 C 60)
    c)  (330 C  60) / (360 C 60)
    d) 1/12
3) There exist 3 different months such that exactly 20 days are selected from each one of these months.
    a) (30 C 20)^3 / (360 C 60)
    b) (90 C 60) / (360 C 60)
    c) ((12 C 3) * (30 C 20)^3) / ( 360 C 60)
    d) 1/4

NOTE: n C k = n! / k! (n - k)!