Question

What's the probability that a 31 day month will have five Mondays? (Assume that there is equal chance of any one of the seven days being the first day of the month).

*Just a little note, I think we're supposed to use permutations or combinations for this, as it's a question under that topic we're to do.

Answer 1

we have complete 4 weeks in the first 28 days of the month. We have 3 more days x = 29th day, y = 30th and z = 31st days of the month.

  x, y, z  can be any week day.

permutations possible:
    If x is known then y and z are consequently fixed. There are 7 possible permutations for x.    Hence, total number of permutations/combinations / possibilities are :  7
      Sat  Sun  Mon,  Sun Mon Tue,  Mon Tue Wed,  
      Tue Wed Thu,  Wed Thu Fri,   Thu Fri Sat,  Fri Sat Sun

The desired outcomes/permutations are the first three in the above list.
      Sat Sun Mon,  Sun Mon Tue,   Mon Tue  Wed

probability =  3 / 7