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?

i don't knw how to do this kind of problems..can anyone teach me???

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.

To solve this problem, we can use the concept of combinations. Let's break it down step by step.

Step 1: Find the number of combinations of three aces out of the four aces in the deck.
To calculate this, we can use the formula for combinations: nCr = n! / r!(n-r)!, where n is the total number of items and r is the number of items to be chosen.

In this case, we have four aces in the deck (n=4) and we need to choose three aces (r=3). Plugging these values into the formula, we get:
4C3 = 4! / (3! * (4-3)!) = 4! / (3! * 1!) = 4

So, there are four different combinations of three aces that can be drawn from the deck.

Step 2: Find the number of combinations of two kings out of the four kings in the deck.
Similarly, using the same formula, we have four kings (n=4) and we need to choose two kings (r=2). Plugging these values into the formula, we get:
4C2 = 4! / (2! * (4-2)!) = 4! / (2! * 2!) = 6

So, there are six different combinations of two kings that can be drawn from the deck.

Step 3: Multiply the number of combinations of three aces by the number of combinations of two kings to get the total number of different 5-card poker hands possible.
Multiplying the two values, we get:
4 * 6 = 24

Therefore, there are 24 different 5-card poker hands possible consisting of 3 aces and 2 kings.

Remember, in this problem, we are only concerned with the number of different combinations, not the total number of cards in the deck.