Agenda

<aside> 📌 Reminders

• Last assignment! Due December 1, 2024 </aside>

The Product Rule

• If a procedure can be broken down into a sequence of $m$ tasks, and
• there are $n_1, n_2, \dots, n_m$ ways to do the tasks,
• then there are $n_1 \cdot n_2 \cdot \dots \cdot n_m$ ways to do the procedure.

The Sum Rule

• If a task can be done in:
  • one of $n_1$ ways, or
  • one of $n_2$ ways, or
  • ...
  • one of $n_m$ ways,
• where none of the sets of $n_i$ ways overlap,
• then there are $n_1 + n_2 + \dots + n_m$ ways to do the task.

The Subtraction Rule

• If a task can be done in:
  • one of $n_1$ ways, or
  • one of $n_2$ ways,
• and the set of $n_1$ ways and $n_2$ ways overlap, with $n$ ways in common,
• then there are $n_1 + n_2 - n$ ways to do the task.

The Division Rule

• If a task can be done using a procedure:
  • Which can be carried out in $n$ ways, but
  • For each way, exactly $d$ of $n$ ways correspond to one result,
• Then there are $n/d$ ways to do the task.