when the order does not matter, it is a combination.
Permutation
1. Repetition is allowed:
Such as a permutation lock, the number is '333'.
For example, choose 3 of those things(n), the permutations are:
n*n*n
2. No repetition:
For example the three first people in a running race, you can't be first and second, assume there are five people, the permutations are:
5*4*3
!5 / !(5-3)
choose r from n:
!n / !(n-r)
Combination
1. Repetition is allowed
There are five flavors of ice cream: banana, chocolate, lemon, strawberry, vanilla.
We have three scoops, how many variations will there be?
let's use letters for the flavors: {b, c, l, s, v}. Examples selections include:
1. {c,c,c} {three scoops chocolate}
>ooo>>>
2. {b,l,v} (one each of banana, lemon, vanilla)
o>>o>>o
3. {b,v,v} (one scoop of banana, two scoop of vanilla)
o>>>>o
!n / !r * !(n - r)
!(3 + 5 - 1) / !3 * !(5 - 1)
!(r + n - 1) / !r * !((r + n - 1) - r) = !(r + n - 1) / !r * !(n - 1)
2.No repetition
choose 3 from 3
the permutations are:
123
132
213
231
312
321
the combinations are:
123
3! / !(3-3)*!3
choose r from n:
n! / !(n-r)*!r
Permutation
1. Repetition is allowed:
Such as a permutation lock, the number is '333'.
For example, choose 3 of those things(n), the permutations are:
2. No repetition:
For example the three first people in a running race, you can't be first and second, assume there are five people, the permutations are:
Combination
1. Repetition is allowed
2.No repetition