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Answer:
What is the total number of possible hands?
For this case n = 52 and x =3 and if we replace we got:
So then we have a total of 22100 ways in order to select 3 cards from a total of 52 cards.
What is the total number of possible hands if the hand contains exactly one heart?
For the possible cases we can do this:
Since we have 13 hearts and we want to select 1 and the two remain cards are non hearts. So we have 9633 ways in order to have only one heart in a hand of 3, and the probability would be:
Step-by-step explanation:
What is the total number of possible hands?
For this case we assume that w ehave an standard deck of 52 cards and we want to know on how many ways we can select 3 cards from the total of 52, so for this case since the order no matter we can use the formula for combination given by:
For this case n = 52 and x =3 and if we replace we got:
So then we have a total of 22100 ways in order to select 3 cards from a total of 52 cards.
What is the total number of possible hands if the hand contains exactly one heart?
For this case we need to remember that in a tandard deck we have 13 hearts and we want that in the 3 selected card we have just one heart, and we can find this probability using the definition of empirical probability:
Where the total cases on this case are 22100
For the possible cases we can do this:
Since we have 13 hearts and we want to select 1 and the two remain cards are non hearts. So we have 9633 ways in order to have only one heart in a hand of 3, and the probability would be: