Assuming you've got a deck of 40 cards (Ace, 2,3,4,5,6,7,jack,queen,king of 4 colors): How many hands of 10 cards can you make, where you need to have at least one jack and one king, that must be of the same color? Here's how I tried to answer this question. The number of king/jack combinations you can make is 4. You then have 8 cards left, so you multiply 4 by the number of different possible hands of 8 cards possible, while taking in consideration there are only 38 cards left. You get 4((38!)/30!) Then you must take in account the fact that the order of the cards doesn't matter. Thus you divide everything by 10!, the number of different permutations of the whole thing. So you have (4.38!)/((10!)(30!)) Which gives me a decimal number, which tells me I've done something wrong. Anyone mind helping?
