Counting without double counting, and the pigeonhole principle
Count the pupils in two clubs without counting the ones in both twice, count the multiples of 2 or 3, then use the pigeonhole principle to be sure that two things share a box.
- إيران: الصف ١١
- روسيا: الصف ٨
لم يُترجَم هذا المختبر إلى هذه اللغة بعد.
الدليل
This studio follows the Iranian grade 11 and 12 counting topics: the inclusion–exclusion principle and the pigeonhole principle.
When you add the sizes of two sets, the members that are in both are counted twice. So the number in at least one set is n(A) + n(B) − n(A ∩ B).
For the pigeonhole principle, think of the worst case: if you have more things than boxes, you can be sure that some box has two. Common mistakes: forgetting to subtract the overlap, answering with the number of boxes instead of one more, and rounding the average down.