what formula or how do i solve for this:
How many 5-card poker hands containing of 2 aces and 3 kings are possible with an ordinary 52-card deck?
(4*3*2)/3! combinations of three kings x (4*3)/2)combinations of two aces = 24.
Well, solving this problem requires some serious card skills, so let's shuffle our way to the solution!
First, we need to find the number of combinations of three kings. Since there are 4 kings in a deck, we can choose 3 of them in a specific order, which is (4 choose 3). But since order doesn't matter (we're not playing poker juggling here), we divide by the factorial of 3.
Now, for the two aces. In a 52-card deck, we have 4 aces, so we can choose 2 of them in a specific order, which is (4 choose 2). But remember, order doesn't matter, so we divide by the factorial of 2.
By multiplying these two results together, we get the total number of 5-card poker hands containing 2 aces and 3 kings. Drumroll, please... and the answer is 24!
So, the probability of getting a hand like that is about as likely as finding a unicorn riding a unicycle.
To solve the problem, we need to use the concept of permutations and combinations.
Step 1: Calculate the number of ways to select 3 kings out of 4.
There are 4 kings in a deck, and we need to select 3 of them. This can be done using combinations. The formula for combinations is given by nCr = n! / (r!(n-r)!), where n is the total number of objects to choose from, and r is the number of objects to be chosen.
In this case, n = 4 (number of kings) and r = 3 (number of kings to be chosen).
Therefore, the number of ways to select 3 kings out of 4 is calculated as:
4C3 = 4! / (3! * (4-3)!) = (4 * 3 * 2) / (3 * 2) = 4.
Step 2: Calculate the number of ways to select 2 aces out of 4.
Similarly, for a deck of cards, the number of ways to select 2 aces out of 4 can be calculated using combinations.
In this case, n = 4 (number of aces) and r = 2 (number of aces to be chosen).
Therefore, the number of ways to select 2 aces out of 4 is calculated as:
4C2 = 4! / (2! * (4-2)!) = (4 * 3) / (2) = 6.
Step 3: Calculate the total number of 5-card poker hands with 2 aces and 3 kings.
The two events, selecting 3 kings and 2 aces, are independent of each other. Thus, we multiply the number of ways for each event.
The total number of 5-card poker hands with 2 aces and 3 kings is then calculated as:
Number of ways to select 3 kings * Number of ways to select 2 aces = 4 * 6 = 24.
Therefore, there are 24 possible 5-card poker hands containing 2 aces and 3 kings in an ordinary 52-card deck.
To solve this problem, you need to use the concept of combinations.
First, let's break down the problem. We need to find the number of 5-card poker hands that contain 2 aces and 3 kings.
There are 4 aces in a deck, so we have to choose 2 out of those 4 aces for our hand. The number of ways to choose 2 items out of 4 is given by the combination formula: nCr = n! / (r!(n-r)!). In this case, n is 4 (number of aces) and r is 2.
Therefore, the number of combinations of two aces is 4C2 = 4! / (2!(4-2)!) = (4*3) / (2*1) = 6.
Similarly, there are 4 kings in a deck, and we have to choose 3 out of those 4 kings. So, the number of combinations of three kings is 4C3 = 4! / (3!(4-3)!) = (4*3*2) / (3*2*1) = 4.
To find the total number of possible 5-card poker hands containing 2 aces and 3 kings, you need to multiply the number of combinations of two aces and three kings: 6 * 4 = 24.
Therefore, there are 24 possible 5-card poker hands containing 2 aces and 3 kings in an ordinary 52-card deck.