Addition Counting Principle
Calculate Addition Counting Principle in Grade 10 math: apply factorial formulas and counting methods to solve combinatorics problems with Saxon Algebra 2.
Key Concepts
Suppose a trial can result in any of $n 1$ outcomes from one category, any of $n 2$ outcomes from another category, and so on. If there are $k$ different categories of outcomes, then the total number of outcomes that can result is $n 1 + n 2 + \ldots + n k$.
Draw a king or a queen from a standard deck: 4 kings + 4 queens = 8 possible outcomes. From numbers 1 20, choose a perfect square or a multiple of 7: \{1, 4, 9, 16\} or \{7, 14\}. This gives $4 + 2 = 6$ total outcomes.
Common Questions
What is the Addition Counting Principle?
If event A can occur in m ways and event B in n ways, and they cannot occur simultaneously (mutually exclusive), then A or B can occur in m + n ways total.
When do you use addition vs multiplication counting principles?
Use addition when choosing between options (OR). Use multiplication when combining sequential choices (AND). Picking shirt OR pants uses addition; picking shirt AND pants outfit uses multiplication.
How do you apply the Addition Counting Principle in Grade 10 math?
List all mutually exclusive options and add their counts. If choosing between 4 red shirts or 3 blue shirts, you have 4 + 3 = 7 total choices, since you pick one or the other.