Respuesta :
Answer:
49,766,400
Step-by-step explanation:
To distribute 13 cards to each of the 4 players so that each player has a Queen (Q), King (K), and Jack (J) of the same suit, we can follow these steps:
Step 1: Choose the suit
Since each player needs to have the same suit, we first must choose one of the four suits (clubs, diamonds, hearts, or spades). Let's say we choose the club suit.
Step 2: Choose the Q, K, and J for each player
In a deck of cards, there is one Q, one K, and one J for each suit. So for each player, we need to distribute one Q, one K, and one J of the chosen suit (clubs).
For the first player, we have 13 choices for the Q, 12 choices for the K (since we already distributed one card), and 11 choices for the J (since we distributed two cards). This gives us a total of 13 * 12 * 11 = 1,716 possible combinations for the Q, K, and J of the club suit for the first player.
Similarly, for the second player, we have 10 choices for the Q (since we distributed three cards), 9 choices for the K, and 8 choices for the J. This gives us a total of 10 * 9 * 8 = 720 possible combinations for the Q, K, and J of the clubs suit for the second player.
For the third player, we have 7 choices for the Q, 6 choices for the K, and 5 choices for the J. This gives us a total of 7 * 6 * 5 = 210 possible combinations for the Q, K, and J of the club suit for the third player.
Finally, for the fourth player, we have 4 choices for the Q, 3 choices for the K, and 2 choices for the J. This gives us a total of 4 * 3 * 2 = 24 possible combinations for the Q, K, and J of the clubs suit for the fourth player.
Step 3: Multiply the combinations
To find the number of ways to distribute the cards, we multiply the number of combinations for each player. So the total number of ways is:
1,716 * 720 * 210 * 24 = 49,766,400
Therefore, there are 49,766,400 ways to distribute 13 cards to each of the 4 players so that each player has a Q, K, and J of the same suit
