Final answer:
The probability of being dealt two jacks and three tens from a standard deck is calculated using combinations. The calculation yields a probability of 1/108,290, which is not one of the given options, indicating a possible error in the options or question.
Step-by-step explanation:
The probability of being dealt two jacks and three tens from a standard deck can be calculated by considering the number of ways to choose the jacks and tens separately and then combining them, all divided by the total number of ways to choose any five cards from the deck.
To calculate the number of ways to get two jacks, we choose 2 jacks from the 4 available, which can be done in C(4,2) ways. For the tens, we also choose 3 tens from the 4 available, which can be done in C(4,3) ways. The total number of ways to choose 5 cards from a 52 card deck is C(52,5).
Using combinations:
- Number of ways to choose 2 jacks: C(4,2) = 4! / (2! * (4 - 2)!) = 6 ways
- Number of ways to choose 3 tens: C(4,3) = 4! / (3! * (4 - 3)!) = 4 ways
The probability is therefore (6 * 4) / C(52,5).
We calculate C(52,5) as follows: C(52,5) = 52! / (5! * (52 - 5)!) = 2,598,960 ways
Thus, the probability = (6 * 4) / 2,598,960 = 24 / 2,598,960 which simplifies to 1 / 108,290, which is not an option given in the original question. Therefore, there might be an error in the provided options, or we may need to recheck the question.