lionely said:Homework Statement
How many different hands of 13 cards can be obtained containing at least 12 hearts?
Homework Equations
The Attempt at a Solution
I'm confused, well I know there could be a possibility of getting 13 hearts, but I am getting confused trying to work out the other possibilities.
lionely said:Well, because wouldn't each of the 40 cards left to be chosen from be a choice? I'm not sure how to express it
lionely said:Sorry aren't there 39 choices for the nonheart? and the number of ways of picking 39 nonhearts would it just be 39 ways?
lionely said:Sorry , for my poor English. Well to pick 12 hearts out of 13... that would be 13C12 so... 13 ways.
So the total amount of ways would be (13 x 39) + that one way of picking all 13 hearts?
There are 635,013,559,600 possible combinations of 13-card hands.
The probability of having at least 12 hearts in a 13-card hand is approximately 0.00000003%.
Yes, it is possible to have exactly 12 hearts in a 13-card hand. This would mean that the remaining card in the hand is not a heart.
The probability of having exactly 12 hearts in a 13-card hand is approximately 0.00000002%.
The probability of having at least 12 hearts in a 13-card hand will decrease as the number of cards in the hand increases, as there are more possible combinations to choose from. However, the exact probability will depend on the specific number of cards in the hand.