Learn math, science, English SAT & ACT from
highquaility study
videos by expert teachers
Thank you for watching the preview.
To unlock all 5,300 videos, start your free trial.
Combinations  Problem 4
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
Choosing in probability come in a lot when we're dealing with card games, so what we're looking at now is a probability of being dealt a heart flush in poker. And for those of you who don't play poker, what a heart flush means is you're dealt all hearts in a poker hand which is a 5 card hand.
So we are dealing with probability which tells us we have to do the ratio of the number of events that we want over the total number of potential events, we're dealing with a fraction. And the total number of events are just any possible poker hand that we can be dealt. There are 52 cards in a deck and so basically what we're dealing with is 52 choose 5, we're choosing 5 of them. The order we are dealt doesn't matter, so therefore I know it's a choose 52 cards in a deck choose 5 for your hand. So that's your total number of outcomes.
What we're then concerned with is the ways of being dealt a heart flush. Heart flush tells us all of our cards are hearts, so we know that we need to choose 5 to make our hand and what we're choosing 5 out of is only the hearts. So there are 52 cards in a deck 4 sits so 52 divided by 4 is the number of hearts which turns out ot be 13. So there are 13 choose 5 ways of getting only heart cards and there are 52 choose 5 different ways of being dealt a different hand and whatever this ratio is is going to be the probability of getting a hand completely filled with hearts.
Please enter your name.
Are you sure you want to delete this comment?
Carl Horowitz
B.S. in Mathematics University of Michigan
He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his stepbystep explanations are easy to follow.
Concept (1)
Sample Problems (4)
Need help with a problem?
Watch expert teachers solve similar problems.

Combinations
Problem 1 7,106 viewsHow many ways to choose 3 students from a class of 20.

Combinations
Problem 2 6,187 viewsA catering menu gives you the choice of 3 out of 7 apps, 4 out of 12 main courses, and 3 out of 5 desserts.
How many different orders? 
Combinations
Problem 3 5,589 viewsIn a recent school election 40 students voted for candidate A and 60 voted for candidate B.
If 8 students are chosen at random find the probability 5 voted for candidate B? 
Combinations
Problem 4 5,562 viewsFind the probability of being dealt a heart flush in poker.
Comments (0)
Please Sign in or Sign up to add your comment.
·
Delete