*Use mathematical induction to prove the product rule for m tasks from the product rule for two tasks.*
The Product Rule for counting states: The Product Rule: Suppose that a procedure can be broken down into a sequence of two tasks. If there are n1 ways to do the first task and for each of these ways of doing the first task, there are n2 ways to do the second task, then there are n1n2 ways to do the procedure.
Base Case: I choose P(m) = 4, which is the product rule for two tasks.
Induction: I am using P(m) and consider P(m+1). My inductive hypothesis (guessing here) can be n1* n2 * ...*nm * nm+1,
How do I prove this further in words or math computation? Thanks for any help.