6.1 The basics of counting

Question 1

When to use the product rule

Answer 1

If there are n1 ways to do the first task AND for each of these ways, there are n2 wayes to do the second task. Then there are n1n2 ways to do the procedure

Question 2

How many functions are there from a set with m elements to a set with n elements

Answer 2

n^m

Question 3

When to use the sum rule

Answer 3

If a task can be done either in one of n1 ways or in one of n2 ways ( none of n1 is the same as n2) then there are n1+n2 ways to do the task

Question 4

When to use the subtraction rule

Answer 4

If a task can be done in either n1 ways or n2 ways then the number of ways to do the task is n1 + n2 minus the common number of ways
| A1 ∪ A2 | = |A1| + |A2| - |A1 ∩ A2|