What is the probability of being dealt 3 tens and 2 kings from a deck of cards?

number of ways to get 3 tens and 2 kings

= C(4,3) * C(4,2)
= 24

prob(of your event) = 24/C(52,5)
= 24/2598960
= 1/108290

Well, let's face it, the chances of being dealt 3 tens and 2 kings from a deck of cards are pretty slim. In fact, it's like trying to find a needle in a haystack while blindfolded and wearing oven mitts. But if you really want the probability, I guess I can give it to you. There are 4 tens and 4 kings in a standard deck, so the probability of getting a ten on the first draw is 4/52. Then, after you've successfully picked a ten, there are only 3 tens left in the deck, so the probability of getting a ten on the second draw is 3/51. Multiply those probabilities together, and you get the probability of getting two tens in a row, which is a whopping (4/52) * (3/51). Now, let's move on to the kings. After you've already picked two tens, there are only 4 kings and 49 cards left in the deck. So the probability of getting a king on the third draw is 4/50, and on the fourth draw, it's 3/49. Multiply those probabilities together, and you get (4/50) * (3/49), the probability of getting two kings in a row. Finally, to find the probability of getting 3 tens and 2 kings, you just have to multiply the probability of getting two tens with the probability of getting two kings: (4/52) * (3/51) * (4/50) * (3/49). Now, if you'll excuse me, my brain hurts from all this math.

To find the probability of being dealt 3 tens and 2 kings from a deck of cards, we need to calculate the probability of getting 3 tens and 2 kings out of the total number of possible 5-card hands.

Step 1: Find the number of ways to choose 3 tens out of 4 tens:
There are 4 tens in a standard deck of cards, so we use the combination formula to calculate the number of ways to choose 3 out of 4:
C(4, 3) = 4! / (3! * (4-3)!) = 4

Step 2: Find the number of ways to choose 2 kings out of 4 kings:
There are 4 kings in a standard deck of cards, so we use the combination formula to calculate the number of ways to choose 2 out of 4:
C(4, 2) = 4! / (2! * (4-2)!) = 6

Step 3: Calculate the total number of 5-card hands from a deck of 52 cards:
There are C(52, 5) = 52! / (5! * (52-5)!) = 2,598,960 possible 5-card hands.

Step 4: Calculate the probability:
The probability of being dealt 3 tens and 2 kings is equal to the number of favorable outcomes (4 tens and 2 kings) divided by the total number of possible outcomes (2,598,960 hands):
Probability = (4 * 6) / 2,598,960 ≈ 0.00007365

Therefore, the probability of being dealt 3 tens and 2 kings from a deck of cards is approximately 0.00007365.

To calculate the probability of being dealt 3 tens and 2 kings from a deck of cards, we first need to determine the total number of possible outcomes.

There are 52 cards in a deck, so the total number of possible outcomes can be calculated using the combination formula:

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

In this case, we want the combination of 5 cards from a deck of 52, so n = 52 and r = 5:

C(52,5) = 52! / (5!(52-5)!)

Simplifying the equation:

C(52,5) = (52! / (5!47!)) = 2,598,960

Now, we need to determine the number of favorable outcomes, which is the number of ways we can select 3 tens and 2 kings from the deck.

The deck contains 4 tens and 4 kings, so we need to select 3 tens from 4 and 2 kings from 4:

C(4,3) * C(4,2) = (4! / (3!(4-3)!)) * (4! / (2!(4-2)!)) = (4 * 3 * 2 * 1) / (3 * 2 * 1) * (4 * 3) / (2 * 1) = 4 * 6 = 24

Therefore, the number of favorable outcomes is 24.

To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 24 / 2,598,960 ≈ 0.00000925 or 0.000925%

So, the probability of being dealt 3 tens and 2 kings from a deck of cards is approximately 0.000925% or 0.00000925.