Sum and Product Rules

Theproduct ruleprovides a way to countntuples created from pairing items in sets.

In contrast, thesum ruleis applied when there are multiple choices from different setsbut only one selection is made.

1.Bit Strings

How many bit strings of length 8 end in 1?

8!1=40319

2⁸1=255

2⁷=128

or 7!=5040

2.Strings

How many strings of length 5 are there over the alphabet {x,y,z} that begin with x and end with x ?

3!=6

3³=27

23³=54

or 3⁴=81

3.Strings

How many strings of length 5 are there over the alphabet {x,y,z} that either begin with z or end with z ?

3⁵2=241

3⁴+3⁴3³=135

23⁴2=324

or 5²3=23