In a game, each person is dealt 3 cards from a deck of 52 cards and a player…
2024
In a game, each person is dealt 3 cards from a deck of 52 cards and a player is said to have a winning deck if and only if he or she has a king, a queen and a jack each, irrespective of the colour or the sign. What is the total possible number of winning decks for this game?
- A.
3
- B.
4
- C.
16
- D.
64
Show answer & explanation
Correct answer: D
Concept: When items are selected independently from several distinct groups, the total number of ways to make one selection from each group is the product of the number of ways to choose from each group individually (the fundamental principle of counting).
A winning deck needs exactly one king, one queen, and one jack, with the suit not mattering. The three choices are made independently:
There are 4 kings in the deck (one per suit), so choosing 1 king can be done in 4C1 = 4 ways.
Similarly, there are 4 queens, so choosing 1 queen can be done in 4C1 = 4 ways.
Similarly, there are 4 jacks, so choosing 1 jack can be done in 4C1 = 4 ways.
Since the three choices are independent, multiply the counts: 4 × 4 × 4 = 64.
Cross-check: this is equivalent to independently picking one of the 4 suits for each of the three fixed ranks (king, queen, jack), giving 4 × 4 × 4 = 64 — the same result confirms the count.
So, the total number of winning decks possible is 64.