To find out how many ways you can choose an ace, king, queen, and jack from an ordinary deck of 52 cards, we need to consider two cases: when the cards must be of different suits and when they must be of the same suit.
1. Different Suits:
In this case, we need to choose one card from each suit: diamonds, hearts, clubs, and spades. Since each suit has 13 cards (ace, king, queen, and jack), we have 13 choices for the first card, 13 choices for the second card, 13 choices for the third card, and 13 choices for the fourth card. To find the total number of combinations, we multiply these choices together: 13 * 13 * 13 * 13 = 28,561.
2. Same Suit:
In this case, we need to choose all four cards from the same suit. Since each suit has 13 cards, we have 13 choices for the first card, 12 choices for the second card (as we have already chosen one card), 11 choices for the third card, and 10 choices for the fourth card. Again, we multiply these choices to find the total number of combinations: 13 * 12 * 11 * 10 = 15,120.
Therefore, the number of ways you can choose an ace, king, queen, and jack from an ordinary deck of 52 cards, for the different suits and same suit cases, are as follows:
- Different Suits: 28,561 ways.
- Same Suit: 15,120 ways.