Table of Contents
Definitions
- a Combination is when the order doesn’t matter.
- a Permutation is When the order does matter.
In other words:
A Permutation is an ordered Combination.
Permutations
There are 2 types of permutation:
- Permutation with Repetition: such as the lock. It could be “444”.
- Permutation without Repetition: for example the first three people in a running race. You can’t be first and second.
Permutation with Repetition
The formula is written:
nr
where,
- n is number of things to choose from
- r is number of things we choose of n
- repetition is allowed
- order matters
Permutation without Repetition

where,
- n is number of things to choose from
- r is number of things we choose of n
- repetition is NOT allowed
- order matters
Permutation Examples
1. For my account pin, there are 10 numbers to choose from (0,1,2,3,4,5,6,7,8,9) and we choose 6 of them. (You can choose same number twice or more)
nr = 10 × 10 × 10 × 10 × 10 × 10 = 1,000,000
So there are 1,000,000 permutations for my pin.
2. What order could 7 runners be in top 3? (the runner in first place can’t be in second place)

So there are 210 permutations for top 3 runners.
Permutation Notation
Instead of writing the whole formula, people use different notations such as these:
P(n,r) = nPr = nPr =
P(7,3) = 210
Combinations
There are 2 types of combinations (remember the order does not matter now):
- a combination with Repetition: such as coins in your pocket (5,5,10,10,10)
- a combination without Repetition: such as lottery numbers (5,14,17,22,30,34)
Combination with repetition
The formula is written:

where,
- n is number of things to choose from
- r is number of things we choose of n
- repetition is allowed
- order doesn’t matters
Combination without repetition
The formula is written:

where,
- n is number of things to choose from
- r is number of things we choose of n
- repetition is NOT allowed
- order doesn’t matters
Combination Examples
1. There are strawberries, grapes, bananas, pineapples, and apples in refrigerator. I Want to make 3 cups of juice. How many combinations i can make? (repetition is allowed)

So, there are 420 combinations of juices i can make.
2. My teacher tell me to choose 3 girls from 7 girls in my class. How many choices i have? (repetition is not allowed)

Combination Notation
Instead of writing the whole formula, people use different notations such as these:
C(n,r) = nCr = nCr =
C(7,4) =35