[EzExZeRo7497]

There are 20 ways (5! / 3!) to have three hearts on the board, 5 ways (5! / 4!) to have 4 hearts on the board, 1 way to have 5 hearts on the board.

P(3 hearts) = (39/52 * 38/51 * 13/50 * 12/49 * 11/48) * 20 = 16.3085%
P(4 hearts) = (39/52 * 13/51 * 12/50 * 11/49 * 10/48) * 5 = 1.07293%
P(5 hearts) = (13/52 * 12/51 * 11/50 * 10/49 * 9/48) = 0.049519807%

Edit: Actually not sure about the three hearts one...