Khan Academy on a Stick
Probability and combinatorics
Permutations and combinations. Using combinatorics to solve questions in probability.

Permutations
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Introduction to permutations

Combinations
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Introduction to combinations

Example: Ways to arrange colors
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Thinking about how many ways you can pick four colors from a group of 6

Example: 9 card hands
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Thinking about how many ways we can construct a hand of 9 cards

Example: Ways to pick officers
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How many ways can we pick officers for our organization?
Permutations and combinations
You want to display your Chuck Norris dolls on your desk at school and there is only room for five of them. Unfortunately, you own 50. How many ways can you pick the dolls and arrange them on your desk? What if you don't care what order they are in or how they are posed (okay, of course you care about their awesome poses)?

Example: Probability through counting outcomes
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The probability of getting exactly 2 heads when flipping three coins. Thinking about this by visualy depicting all of the outcomes.

Example: All the ways you can flip a coin
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Manually going through the combinatorics to determine the probability of an event occuring

Getting Exactly Two Heads (Combinatorics)
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A different way to think about the probability of getting 2 heads in 4 flips

Probability and Combinations (part 2)
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Making at least 3 out of 5 free throws.

Probability using Combinations
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Probability of getting exactly 3 heads in 8 flips of a fair coin.

Exactly Three Heads in Five Flips
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Probability of exactly 3 heads in 5 flips using combinations

Example: Different ways to pick officers
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Thinking about the different ways we can pick officers in order to find the probability of one situation in particular.

Example: Combinatorics and probability
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Probability of getting a set of cards

Example: Lottery probability
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What is the probability of winning a 4number lottery?

Mega Millions Jackpot Probability
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Probability of winning the Mega Millions jackpot

Generalizing with Binomial Coefficients (bit advanced)
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Conceptual understanding of where the formula for binomial coefficients come from

Conditional Probability and Combinations
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Probability that I picked a fair coin given that I flipped 4 out of 6 heads.

Conditional Probability (Bayes Theorem) Visualized
Conditional probability visualized using trees.

Birthday Probability Problem
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The probability that at least 2 people in a room of 30 share the same birthday.
Probability using combinatorics
This tutorial will apply the permutation and combination tools you learned in the last tutorial to problems of probability. You'll finally learn that there may be better "investments" than poring all your money into the Powerball Lottery.