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.
\[\sum_{i=1}^{n}a_i=a_1+a_2+\cdots+a_n\]
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.
\[b_1b_2\cdots b_n\]
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