3 People, 5 Hats

There are 3 people in a room; let's call them A, B, and C. In the room is a box with 5 hats - exactly 3 red hats and 2 blue hats. Each person is randomly called to place a hat on their head. They then stand in a room facing each other such that each person can see the other two but cannot see his own hat. Now, we ask each of them the color of their hat. A goes first, and says, "I don't know." After hearing that A doesn't know, B also admits he doesn't know. C then says, with conviction: "I know the color of my hat!"

Here's the catch: C is blind! What is the color of his hat, and how does he know?

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