Suppose you have 52 cards and know that you are in a state where the only cards you draw are 2,3,4,5,6,7,8,9,10. You draw 4 cards from the 52 cards (36 considering the state you know you are in). What is the chance that the sum of black cards drawn is twice that of red cards?
One way to approach the problem is to split by the number of black cards drawn. For pairs of red and black cards (R,B) we can either have (2,2) or (1,3). We can then count, for each of the 9 values, each case for which the black cards are twice the sum of the red ones. The case (3,1) has no solutions. Is there a less tedious way to approach this?