This question type involves solving combination equations using the symmetry property and selecting groups with fixed (required) members.
If , then:
This property is used to solve equations involving combinations.
Example: If , find .
Solution: Since , we use :
When certain members must be included in a selection:
where:
Example: In how many ways can a team of 4 be chosen from 7 people if one specific person must always be included?
Solution: Fix the 1 required person. Choose the remaining from the remaining people:
Answer: 20 ways
When certain members must not be included:
where people are excluded from the pool entirely.