Combinatorics

Combinatorics is about how many combinations there are of different choices.

It could be the number of possible codes with certain digits, or the number of outcomes when rolling dice.

 

It can also be everyday choices, such as e.g. transport to school or which clothes to wear.

 

Counting technique

Either or

When you have to choose between several options, where you can only pick one of them, you use the Addition method (Sum rule).

How many options are there if you have to choose between:

 

• Either: Cycle
• Or: Take the bus (2 different lines)
• Or: Take the train

 

So there are either 1 choice or 2 choices or 1 choice:

 

$$ \large 1+2+1=4\ options $$

 

 

Both and

If you have to combine several choices at the same time, such as f.e. clothing choices, you use the Multiplication method (Product rule).

 

• 3 shirts
• And: 2 pairs of pants
• And: 4 pairs of shoes

 

$$ \large 3 \cdot 2 \cdot 4 = 24\ combinations $$

 

 

Methods

Addition method:

 

$$ Combinations\ = a + b + c.....+\ n $$

 

Multiplication method:

 

$$ Combinations\ = a \cdot b \cdot c.....\ \cdot \ n  $$