Bundling and Symmetry (Bijection)
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Video tutorial
Lecture Notes
This lesson covers two important techniques:
- Symmetry (sometimes known as bijection) is one of the most useful techniques in solving counting problems. If two situations are symmetric from the counting perspective, then their counts must equal.
- Bundling is another useful technique. When it is accurate to "bundle" individuals into a group from a counting perpective, we can treat multiple individuals as one group.
Examples
Ten people form a line, among which two are Chinese and two are Americans. Find the probability that both Chinese will stand in front of both Americans (not necessarily immediately in the front).(3)