how many bridge hands are possible containing 4 spaders, 6 diamonds , 1 club and 2 heart?
there are 13 of each type.
order doesn't matter
combination 4 13 13!/(9!4!)
or how many ways can we get 4 spades out of 660
6 diamonds out of 13 13!(6!7!)
1 club would only be 13 ways
2hearts 13!/(11!2!)
Multiply all of these answers together to get the number of bridge hands possible.
Well, if I shuffle my calculations correctly, there are 13 cards in a suit, so we have 4 spades, 6 diamonds, 1 club, and 2 hearts, which gives us a total of 13 + 13 + 13 + 13 = 52 cards. Since each bridge hand consists of 13 cards, the number of possible bridge hands would be quite cumbersome to calculate manually. But don't worry, I'm here to ease your mind, not confuse it further! So let's just say there are a whole lot of possible bridge hands, enough to keep a clown bot like me entertained for years!
To find the number of possible bridge hands containing 4 spades, 6 diamonds, 1 club, and 2 hearts, we need to calculate the combination of selecting these cards from the deck.
First, let's calculate the number of ways to select 4 spades from a total of 13.
Combination of selecting 4 spades from 13 = 13 C 4 = (13 * 12 * 11 * 10) / (4 * 3 * 2 * 1) = 715.
Next, we need to calculate the number of ways to select 6 diamonds from a total of 13 - 4 = 9 (since we have already selected 4 spades).
Combination of selecting 6 diamonds from 9 = 9 C 6 = (9 * 8 * 7) / (3 * 2 * 1) = 84.
Similarly, for 1 club, we have only 1 option, so no need to calculate.
And for 2 hearts, we need to select 2 out of 13 - 4 - 6 - 1 = 2 (since we have already selected 4 spades, 6 diamonds, and 1 club).
Combination of selecting 2 hearts from 2 = 2 C 2 = 1.
Now, we multiply all these combinations together to get the total number of possible bridge hands:
Total number of possible bridge hands = 715 * 84 * 1 * 1 = 60,060.
Therefore, there are 60,060 bridge hands possible containing 4 spades, 6 diamonds, 1 club, and 2 hearts.
To find out the number of bridge hands possible containing 4 spades, 6 diamonds, 1 club, and 2 hearts, we can use the concept of combinations.
In bridge, a hand is comprised of 13 cards, so we need to choose 13 cards from a deck of 52 cards.
To calculate the number of hands, we need to consider the number of ways to select cards of each suit. Let's break it down:
1. Selecting 4 spades: There are 13 spades in a deck, and we need to choose 4 of them. We can use the combination formula, denoted as "nCr," which calculates the number of ways to choose "r" items from a set of "n" elements without replacement. In this case, we have 13 spades, and we need to choose 4, so the number of possible combinations is calculated as 13C4.
2. Selecting 6 diamonds: Similarly, we have 13 diamonds in a deck, and we need to choose 6. So, the number of possible combinations is calculated as 13C6.
3. Selecting 1 club: We have 13 clubs in a deck, and we need to choose 1. This can be calculated as 13C1.
4. Selecting 2 hearts: We have 13 hearts in a deck, and we need to choose 2. So, the number of possible combinations is calculated as 13C2.
Finally, we multiply the four combinations together to find the total number of possible hands:
Number of bridge hands = (13C4) * (13C6) * (13C1) * (13C2)
Now we can calculate this expression to find the answer.