colors = {Red, Green, Purple};
symbols = {"0", "\[TildeTilde]", "\[Diamond]"};
numbers = {1, 2, 3};
shadings = {"\[FilledSquare]", "\[Square]", "\[DoublePrime]"};

validTripleQ[l_List] := Entropy[l] != Entropy[{1, 1, 2}];
validSetQ[cards_List] := And @@ (validTripleQ /@ Transpose[cards]);

allCards = Tuples[{colors, symbols, numbers, shadings}];

deal[{numDeal_, setNum_}] := Module[{cards, count = 0},
   While[count != setNum,
    cards = RandomSample[allCards, numDeal];
    count = Count[Subsets[cards, {3}], _?validSetQ]];

   cards];

Row[{Style[#2, #1], #3, #4}] & @@@ deal[{9, 4}]