Find the probability of the following five-card poker hands from a 52-card deck. In poker, aces are either high or low.

Four of a kind (4 cards of the same value)

I keep getting 1/199,920, but that's not one of my options.

Suppose you were after the probability of getting four aces in five cards. Suppose also that the four aces were the first four cards out of the five you were dealt. The chances of getting that would be (4/52)x(3/51)x(2/50)x(1/49).

But the 5th card could be any of the five you are dealt, so the above needs to be multiplied by 5. Also, your four of a kind could be any of the 13 different face-values, so multiply the above by 13 to get all of them. That would give you

(13x5x4x3x2)/(52x51x50x49) = 1/4165.
Is that one of your options?

Well, if you keep getting the same result over and over, maybe it's time to change your approach. Let's do some math together.

To calculate the probability of getting a four of a kind in a five-card poker hand, you need to consider two parts: choosing the value of the four matching cards and selecting the fifth card.

First, you choose the value of the four cards, which can be any of the 13 possible card values. So, there are 13 options for the four of a kind.

Next, you must pick one card out of the remaining 48 cards in the deck to complete your hand.

To calculate the probability, you divide the number of favorable outcomes (ways to get a four of a kind) by the total possible outcomes (total number of five-card hands).

The number of favorable outcomes is given by: 13 (options for four of a kind) * 48 (options for the fifth card) = 624.

The total possible outcomes (five-card hands from a 52-card deck) equals the combinations formula: C(52,5) = 2,598,960.

So the probability of getting a four of a kind is: 624 / 2,598,960 ≈ 0.000240%.

It seems like you made an error in your calculation. But hey, good news - the odds are still better than finding a parking spot on a busy Friday night!

To find the probability of getting a four of a kind in a five-card poker hand, we first need to determine the number of possible four of a kind hands and the total number of possible five-card poker hands.

Number of possible four of a kind hands:
There are 13 possible card values (2-10, Jack, Queen, King, Ace), and for each value, there are 4 possible suits (hearts, diamonds, clubs, spades). To form a four of a kind, we choose one card value out of the 13 and then choose any one of the four suits for that value. The fifth card can be any of the remaining 48 cards in the deck. Therefore, the number of possible four of a kind hands is 13 * 4 * 48 = 24,96.

Total number of possible five-card poker hands:
To find the total number of possible five-card poker hands, we need to calculate the combinations of choosing 5 cards out of a deck of 52 cards. This can be calculated using the formula nCr = (n!)/(r!(n-r)!), where n is the total number of items to choose from and r is the number of items to be chosen.

Using this formula, the total number of possible five-card poker hands is: 52C5 = (52!)/(5!(52-5)!) = 2,598,960.

Now, to find the probability of getting a four of a kind, we divide the number of possible four of a kind hands by the total number of possible poker hands:

Probability of getting a four of a kind = Number of possible four of a kind hands / Total number of possible five-card poker hands
= 24,96 / 2,598,960
= 0.00954 (approx.)

So, the probability of getting a four of a kind in a five-card poker hand is approximately 0.00954 or 1/104.

To find the probability of getting a four of a kind in a five-card poker hand, we need to determine the number of favorable outcomes (hands with four cards of the same value) and the total number of possible outcomes.

First, let's calculate the number of favorable outcomes. To form a four of a kind, we need to choose one card value out of the thirteen available in the deck and then select four cards of that value.

- Choose one card value: There are 13 possible card values.
- Select four cards of that value: There are four cards of each value in the deck.

Therefore, the number of favorable outcomes is: 13 * 4 = 52.

Next, let's calculate the total number of possible outcomes. In a five-card poker hand, we are selecting five cards from a standard 52-card deck, so the total number of possible outcomes is the number of combinations of 52 cards taken 5 at a time.

The formula to calculate combinations is:

C(n, r) = n! / (r! * (n-r)!)

where n! represents the factorial of n.

Using this formula, to calculate C(52, 5), we have:

C(52, 5) = 52! / (5! * (52-5)!) = 2,598,960.

Therefore, the probability of getting a four of a kind in a five-card poker hand is:

52 / 2,598,960 = 1 / 49,951.

So, the correct answer is 1/49,951, which is approximately 0.000020004%.

Note that the probability may be rounded for presentation purposes, so it might not exactly match the options given.