Lecture 14: Counting problems using combinations and distributions
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Lesson Summary:
In Lecture 14, you'll learn how to solve counting problems using combinations and distributions. The instructor presents a problem that doesn't appear in any books or problem sets - how many ways are there to order any subset of elements from a set of n? He goes through different cases and shows that the answer is between 2 and 3 times n factorial. The lecture also briefly covers probability and how to calculate the chance of something happening using counting methods.
Lesson Description:
Learn about and solve counting problems using combinations and distributions.
More information about this course:
http://www.aduni.org/courses/discrete
Licensed under Creative Commons Attribution ShareAlike 2.0:
http://creativecommons.org/licenses/by-sa/2.0/
Additional Resources:
- Lecture Notes - Lecture Notes from the course
- Problem Set 6 - A problem set with some problems from this lecture
- Card Trick Problem Set - A problem set with some problems from this lecture
- Card Trick Problem Set Solutions - Solutions to the Problem Set
- Exam 3 - An exam for the current material
Questions answered by this video:
- If you have a set with n elements, how many subsets can you make, how many permutations, and how many ordered subsets are there of the set?
- What is discrete probability and how do you find it?
- What is the probability of rolling four 6s in a row?
- If you are a 50% free throw shooter, what is the probability that you make 5 in a row?
- What is the probability that you make 4 of 5 free throw shots?
- What is the birthday paradox and how do you solve it?
- What is the probability that two or more people in a room have the same birthday?
- If there are 2n socks in a drawer, what is the probability of choosing a pair?
- If two teams both have a 50% chance of winning, what is the probability that the World Series goes 7 games?
- What is conditional probability and how do you calculate it using formulas?
- If you know that a family has two children, and you know that one of the two is a girl, what is the probability that the other is also a girl?
- If you know that the older of two children is a girl, what is the probability that the younger is also a girl?
- Why does probability of a second child beyond a boy / girl change if you know whether the first child is the oldest or not?
- Given that a number is divisible by 5, what is the probability that a random number between 1 and 20 is divisible by 3?
- What are Catalan numbers?
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Staff Review
This lecture has a bunch of more counting problems of different types. Discrete and conditional probability is then explained and found for various situations. Many of the problems have answers that are not intuitive and are quite interesting.
