Problem #4

Later this month (December 6), the 69th William Lowell Putnam Mathematical Competition will be held at universities throughout the United States and Canada. In commemoration, this month's problem is from a previous Putnam.

In the Gregorian calendar:

• A common year contains 365 days; a leap year contains 366.
• Years not divisible by 4 are common years.
• Years divisible by 100 but not by 400 are common years.
• Years divisible by 400 are leap years.

What is the probability that Christmas (December 25) falls on a Wednesday?

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