Mike draws six cards from a standard 52-card deck. What is the probability that he draws a card from at least three of the four suits? Express your answer as a simplified fraction.

1 - (13/16)/(52/6) - (26/52 * 25/21 * 24/50 * 23/49 * 22/48 * 21/47) = 1 - 1716/20358520 - 253/22372 = 774099/783020