Final answer:
To find the number of ways to distribute 13 cards to 4 players including a Queen, King, and Jack of the same suit, use combinatory and permutation principles. The total number of distributions is ¹³C₃ (choose the special cards for the first player) times 4¹⁰ (distribute the remaining cards among 4 players).
Step-by-step explanation:
The question asks for the number of ways to distribute 13 cards, including a Queen, King, and Jack of the same suit, to 4 players from a deck of 52 playing cards. First, we must select 3 specific cards from the first player's hand, which can be done in ¹³C₃ ways (13 choose 3). Then, we have 10 cards left to distribute among the 4 players, with each card having 4 possible players to go to. Hence, each of the 10 cards has 4 choices, giving us 4¹⁰ different ways to distribute them. The total number of ways to distribute the cards is therefore the product of these two quantities: ¹³C₃×4¹⁰.