I have calculated the combination, but I'm just unsure to get the permissions for this question. please assist me
There are 52 cards in a poker deck, excluding the joker. You receive 4 random cards in a poker game. The deck of cards is divided into two suits, hearts, and diamonds, and there are six cards from 7 to K. Identify pair (One pair in the hand plus two random cards) and use four cards to rearrange or guess the final password. (9hearts, 9 diamonds, J hearts, K diamonds are the correct selection, and J hearts, 9 diamonds, K diamonds, 9 hearts are the correct arrangement)
To calculate the number of combinations in this scenario, we need to consider two different steps:
Step 1: Choosing the pair
To identify the pair in the hand, we need to choose one of the ranks (7, 8, 9, 10, J, Q, K) and two of the suits (hearts and diamonds). Since there are 6 ranks and 2 suits, the number of ways to choose the pair is given by the combination formula:
C(6, 1) * C(2, 2) = 6 * 1 = 6
Step 2: Arranging the remaining two cards
After selecting the pair, we have two remaining cards in the hand to be arranged. In this case, these two cards are J hearts and K diamonds. The number of ways to arrange them is 2! (two factorial), which is equal to 2 (since there are only 2 cards).
So, the total number of combinations for this scenario is the product of the number of choices in step 1 and the number of arrangements in step 2:
6 * 2 = 12
Therefore, there are 12 different combinations of pairs (one pair in the hand plus two random cards) in this poker game.
To rearrange or guess the final password, you mentioned two correct selections as "9 hearts, 9 diamonds, J hearts, K diamonds" and "J hearts, 9 diamonds, K diamonds, 9 hearts". However, it's important to note that the concept of "password" is not typically used in poker games. It seems like you are referring to arranging the cards in a specific order or pattern. If you could provide more context or clarify your question, I can assist you further with the specific arrangement you have mentioned.