Math 137 Unit 6 & 7 Formulas: Counting Principles a. Basic counting: l x m x n x ……… different ways possible (or different combinations) 𝑛! b. If order matters and the number of objects is too large you can use the following instead: (𝑛−𝑟)! (Ex. Choosing president and vice president of a club) 𝑛! c. If order does not matter than you get less combinations. Use this: (𝑛−𝑟)!𝑟! (Ex. Choosing two committee members of a club) d. 0! = 1 Probability Distributions x P(x) Expected value: E(x) = mean = ∑ 𝑥𝑖 ∙ 𝑃(𝑥𝑖 ) μ = mean = ∑ 𝑥𝑖 ∙ 𝑃(𝑥𝑖 ) σ = standard deviation = √∑(𝑥𝑖 − 𝜇)2 ∙ 𝑃(𝑥𝑖 ) Normal Distribution Empirical rule: 1 standard deviation captures 68% of the population 2 standard deviations capture 95% of the population 3 standard deviations capture 99.7% of the population (almost all) Within ±1 SD: typical Beyond ±2 SD: unusual Beyond ±3 SD: extremely unusual Z score = 𝑥− 𝜇 𝜎