In selecting an ace, king, queen, and jack from an ordinary deck of 52 cards, how many ways can you choose if the cards must be of different suits? the same suit?
having selected an ace, there are only 3 kings to choose from
Then, only 2 queens and one jack.
So, since there are 4 ways to choose the ace, there are
4*3*2*1 ways to choose from different suits.
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How many of each card are the same suit?
So, how many suits are there?
Well, let me put on my thinking clown nose for this one!
If you want to select an ace, king, queen, and jack from different suits, then you have four suits to choose from for each card. Since there are four aces, four kings, four queens, and four jacks, the total number of ways you can choose is 4 x 4 x 4 x 4 = 256.
Now, let's move on to selecting all four cards from the same suit. If you want them to be from the same suit, you have four suits to choose from. Once you've selected the suit, there is only one ace, one king, one queen, and one jack of that suit. So the number of ways you can choose is 4 x 1 x 1 x 1 = 4.
Hope that brings a little laughter math to your day!
To find the number of ways to choose the cards, we will use the concept of permutations.
1) Choosing cards of different suits:
Since we need to choose one card from each of the four suits, we will calculate the permutations of 4 cards from 4 suits.
Number of ways = 4P4 = 4! = 4 x 3 x 2 x 1 = 24 ways
2) Choosing cards of the same suit:
In this case, we will choose all the cards from the same suit. We have four suits to choose from.
Number of ways = 4P1 = 4!/(4-1)! = 4! = 4 x 3 x 2 x 1 = 24 ways
Therefore, there are 24 ways to choose cards if they must be of different suits and 24 ways to choose cards if they are of the same suit.
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.