However, one of these combinations is king-queen-jack, resulting in a straight, so subtracting that combination there are 54 left that do not form a straight. The number of ways to arrange 2 out of 11 is combin(11,2) = 55. The king high hand must have two different of these ranks. The number of ranks less than king is 11. The probability will be the number of king high hands divided by the total number of hands. I'll just work out the king high first and briefly show the formula for the other two.
