In poker, a "flush" is a five-card hand where all five cards have the same suit. A hand has "three of a kind" when any three cards have the same...

5. In poker, a "flush" is a five-card hand where all five cards have the same suit. A hand has "three of a kind" when any three cards have the same rank. "Four of a kind" is defined analogously. A flush beats a three of a kind, but is beaten by four of a kind. Demonstrate that this ranking of hands corresponds to how unlikely each hand type is to occur when drawing five cards at random (Hint: just count the number of different hands of each type, and then rely on the principle of exchange ability).