How many ways are there to pick 2 different cards from a standard 52 cards deck such that the first card is a spade and the second card is not a Queen?
Answer:
Case I)
First card is not Queen of spade and the other card is any card but not queen.
13-1 * (52-1-4) = 12 *47
Case II)
First card is Queen of spade and the other card is any card but not queen.
1 * (52-4) = 1 * 48
Total ways are: 12*47 + 48 ??
Is this correct?
Best Answer
Yes, your answer is correct: $12 \times 47 + 48 = \boxed{612}$.
Another way of getting the same answer is that there are $13$ spades and $48$ non-queens, $13 \times 48 = 624$. Then you subtract out the times that we picked the same card twice, which is once for every non-queen spade, of which there are $12$. So $624 - 12 = \boxed{612}$.