413 views
4 votes
In how many ways can 13 cards, including a Queen, King, and Jack of the same suit, be distributed to each of 4 players from a deck of 52 playing cards?

(a) ¹³C₃​×4!
(b) ¹³C₃​×4¹⁰
(c) ¹³C₃​×4¹¹
(d) ¹³C₃​×4¹²

User OscarWyck
by
8.3k points

1 Answer

2 votes

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.

Related questions

asked Aug 5, 2022 5.6k views
Stefan Pochmann asked Aug 5, 2022
by Stefan Pochmann
8.3k points
1 answer
4 votes
5.6k views
asked Feb 5, 2024 79.6k views
Ycomp asked Feb 5, 2024
by Ycomp
9.1k points
1 answer
4 votes
79.6k views
1 answer
2 votes
210k views