How often 5 Friday's 5 Saturday's and 5 Sunday's in one month?

Answer 1

I'll guess: 6 times every 7 years on the average ... just a bit less than once a year.

I reason thusly:

-- By looking at a calendar, we notice that in order to have 5 each of

any 3 consecutive weekdays, the month must have 31 days in it.

-- We also notice that there are 7 months in the year that each have

31 days in them.

-- But we also notice that the 7 months with 31 days each, always

begin/end on 6 different days of the week in the course of a year.

Whether it's a regular or a leap year, there's always one day of the

week on which no 31-day month begins, and one day of the week

on which no 31-day month ends.

-- In order to have 5 Fridays, Saturdays, and Sundays in a month, the month

must begin on Friday and end on Sunday.

-- So in any given year, there's a [roughly] 6 out of 7 chance that one of the

months that's long enough will start on a Friday. That means we should see

it happen roughly six times in seven years.

Note:

This isn't exact, because: Since 7 months in the year start on 6 different days

of the week, 2 of them each year have to start on the same day. So any one

given day has a little better than 6 out of 7 chance. But I don't know how to

handle that right now, so I'll go with 6 times in 7 years.

Answer 2

5