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Permutations  Problem 1
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!
So an application of permutations is typically when we are sort of categorizing an event and what we're going to look at now is runners in a race.
So we have 7 runners and what we are looking at is the different ways that they can medal, different ways they could place. And so one way we can do is just by writing out all the different options. We have to have one person to be gold and there are 7 people, so you have 7 people that could be gold, once that person wins one gold, there are now 6 that could get silver and then there is 5 that could get bronze, so what we're going to end up with is 7 times 6 times 5.
But the other way we can do this is doing permutations and basically what that means is just the number of total things we're looking at in this case 7 and then permute the number of things that we are interested. There is 3 people that medal so basically 7 permute 3.
If we were to distribute this out, what we would end up with is 7 times 6 times 5 so for this particular example it would be easy enough to write out our options, but to get used to how the permutation idea works, let's just jump into 7 permute 3, they're both the same thing.
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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.
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Permutations
Problem 1 6,735 views7 runners in a race, how many different ways can they medal?

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Problem 2 5,917 viewsHow many distinct ways are there to arrange the letters in mom?

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Problem 3 5,326 viewsAn ATM pin consists of four numbers. How many pins if
a) repetition is allowed
b) repetition is not allowed 
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Problem 4 4,913 viewsHow many ways can 5 guys and 4 girls be arranged so that guys and girls must alternate?
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