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Combinatorics

Addition Rule

The addition rule says that if you have a set of n items, and a set of m different items, then if you combine the sets you will have n+m items.

Example: Suppose you go to one store that sells brown and black basketballs. You have 2 color options in the first store. Then, in a second store, you find colorful basketballs. There is a red, a purple, and a green ball. You have 3 color options in the second store.

You have 2 options in the first store and 3 options in the second store. So, by the addition rule, you have a total of 5 options:

  1. Brown
  2. Black
  3. Red
  4. Purple
  5. Green




Addition rule stated for sets: If A and B are disjoint, finite sets, then |AB|=|A|+|B|.

Example: Let A={1,3,5} and B={2,8,10,11}. Then |A|=3 and |B|=4.

The union is AB={1,2,3,5,8,10,11}, so |AB|=7. Since 3+4=7, |A|+|B|=|AB|.

Check your understanding:

There are 3 set of shapes:

Which total can be counted using the addition rule?


Unanswered

In a parking garage with 3 floors, floor 1 has 26 cars, floor 2 has 17 cars, and floor 3 has 12 cars. The cars on each floor can be considered a set. How many cars are there in all?