Combination
The arrangement of a given number of items without the consideration of order. Not to be confused with permutations, which is similar but with consideration of order.
Provided:
- the number of distinct items to choose, $n$ (things you have); and
- the number of combinations, $r$ (‘slots’ to fill) $$ ^nC_r = \frac {^nP_r} {r!} = \frac {\frac {n!} {(n-r)!}} {r!} = \frac {n!} {r!(n-r)!} $$
Where restrictions are applicable, it is important to deal with them first. Some common restrictions include:
- the use of binary genders in a group of people.
# Examples
- How many ways are there to select 2 students from a class of 20 students?
- 2 students, 20 students: no detail of order needed
- How many ways are there to choose 5 students from a class of 20 students to participate in a gaming competition?
- 5 students, 20 students: no detail of order needed