Cards are drawn at random from a 52-card deck. Find the number of different 5-card poker hands possible consisting of 3 aces and 2 kings?
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Forget about the fact that there are 52 cards in a deck. The number 52 will not figure in the answer. What matters is that there are four suits to draw from for each number, J, K, K or Ace. The number of combinations of three aces out of four cards is
4!/(3!*1!) = 4
The number of ways of drawing two kings out of four cards is 4!/(2!*2!) = 24/4 = 6
The answer is the product of the number of three-ace combinations and the number of two-king combinations. That number is 24.
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