Addition principle — count by different cases Suppose a task can be completed by mutually exclusive plans A_1,A_2,,A_n, with a_1,a_2,,a_n ways for the respective plans. Since exactly one plan is used, add the numbers of ways. _i=1na_i=a_1+a_2+. s+a_n Multiplication principle — count by different steps Suppose a task is completed through successive steps B_1,B_2,,B_n, with b_1,b_2,,b_n available choices at the respective steps. Multiply the numbers of choices. b_1b_2. s b_n

Addition principle — count by different cases

Suppose a task can be completed by mutually exclusive plans \(A_1,A_2,\ldots,A_n\), with \(a_1,a_2,\ldots,a_n\) ways for the respective plans. Since exactly one plan is used, add the numbers of ways.

\[\sum\limits_{i=1}^{n}a_i=a_1+a_2+\cdots+a_n\]

Addition principle

Multiplication principle — count by different steps

Suppose a task is completed through successive steps \(B_1,B_2,\ldots,B_n\), with \(b_1,b_2,\ldots,b_n\) available choices at the respective steps. Multiply the numbers of choices.

Fundamental Counting Principles

Fundamental Counting Principles