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For that to happen, the month has to be 31 days long and has to start on a Friday. Since there are 7 months with 31 days and one chance in 7 a month will start on a Friday ( roughly, due to leap years) there is about once yaer this will happen.

Next month has 5 Fridays, Saturdays, and Sundays.

Since

14.5% of all years have a January with 5 of (Fri-Sat-Sun),

14.25% of all years have a March with 5 of (Fri-Sat-Sun),

14.5% of all years have a May with 5 of (Fri-Sat-Sun),

14.5% of all years have a July with 5 of (Fri-Sat-Sun),

14.25% of all years have an August with 5 of (Fri-Sat-Sun),

14% of all years have an October with 5 of (Fri-Sat-Sun), and

14% of all years have a December with 5 of (Fri-Sat-Sun),

the average occurrence comes to exactly once per year.

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Q: How often is there 5 Fridays Saturdays and Sundays in one month?
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