How could he have been so sure he was one of them?

Question

Professor Hamilton was visiting his sister, when his young nephew, Theery, showed him a list of all the American Presidents in order. As Hamilton looked at the list he mentioned to Theery that, of the first five American Presidents, (George Washington, John Adams, Thomas Jefferson, James Madison and James Monroe) three died on July 4th, America's Independence Day. Theery looked at the list and said, "I bet that one of the three was James Monroe." Hamilton was surprised that Theery knew this. Since Theery had no knowledge of how or when James Monroe died.
How could he have been so sure he was one of them?

Answer 1

Since Hamilton stated "three of the first five", Theery knew the fifth must be one of the "three" or else Hamilton would have said "three of the first four". He knew the name of the fifth President by reading it off the list.