+130514 We have the number of possible hands that include no queens or one queen.
For the number that include no queens, we want to select 5 cards from any of 12 ranks, not including the queens. So we have C(48,5) =1,712,304
For the number that include one queen, and no more, we want to choose 1 of the 4 queens and then any 4 cards from the other 48. So we have C(4,1)*C(48,4) = 778,320
And adding these together, we get, 2,490,624
+130514 We have the number of possible hands that include no queens or one queen.
For the number that include no queens, we want to select 5 cards from any of 12 ranks, not including the queens. So we have C(48,5) =1,712,304
For the number that include one queen, and no more, we want to choose 1 of the 4 queens and then any 4 cards from the other 48. So we have C(4,1)*C(48,4) = 778,320
And adding these together, we get, 2,490,624
