Why did the British and their American colonies win the contest against the French for control of North America?

The British and the American colonies won the contest for
North America by winning the French and Indian War.  Two major reasons are typically
given to explain why the British were able to win this
war.

First, some scholars argue that the French used up too
much of their military strength fighting in Europe.  The French and Indian War was only
one part of a larger global struggle commonly known as the Seven Years' War.  France is
said to have concentrated on fighting in Europe, thus making it impossible to send
enough troops to fight effectively in North
America.

Second, some scholars point to cooperation between
the British government and the colonies.  The British colonies had many more people than
the French colonies did.  So long as the British colonists were willing to fight, they
could be a formidable force.  Late in the war, the British government finally found a
way to gain the whole-hearted support of the colonies (by giving them more control of
the conduct of the war).  This gave the British a stronger force to fight in
America.

These are two reasons typically given for why the
British won this war.