Introduction to Probability · 免费预览
计数、乘法法则与二项式系数
乘法法则、有序与无序抽取的抽样表，以及二项式系数及其恒等式。
1. The multiplication rule
The multiplication rule
2. The sampling table
The sampling table
3. Working with binomial coefficients
Working with binomial coefficients
4. Choosing the right scheme
From a standard 52-card deck you draw 5 cards and keep them, caring only about which cards end up in your hand. Which count is correct?
5. Pascal recursion by story
The identity Binomial(n, k) = Binomial(n-1, k) + Binomial(n-1, k-1) has a direct committee story. What split does it use?
6. Counting passwords
A password consists of 4 symbols, each a lowercase letter a-z or a digit 0-9. Repeats are allowed. How many passwords are possible? Enter the integer.
7. Gold medals
In an 8-runner race, gold, silver and bronze go to distinct runners, in order of finish. How many medal outcomes are possible? Enter the integer.
8. A bookshelf identity
Using the binomial theorem with x = 1 and y = 2, the sum of Binomial(5, k) times 2 to the k, for k from 0 to 5, equals (1 + 2)^5. What is that value? Enter the integer.
9. In your own words
In your own words, state the most important definition, theorem or method of this lesson and explain what it says.