Induction: I am using P(m) and consider P(m+1). My inductive hypothesis (guessing here) can be n1* n2 * ...*nm * nm+1, [/quote]
Okay, assuming P(m) is "there are [tex]n_1[tex] ways to do task 1, ways to do task 2, ..., to do task m, then there are ways to do all m tasks.
Let "task A" be "do all m tasks". The induction hypothesis, above, says there are ways to do task A. If there are then ways to do task m+1, what does the basis "counting principle" say about the number of ways to do task A and task m+1?How do I prove this further in words or math computation? Thanks for any help.