Combinatorics and Probability
This chapter contains exercises with a wide range of difficulty, where the emphasis is often on the reasoning, not just the final answer. As both Combinatorics and Probability are among the less intuitive topics, students often struggle with it and need significant support from their teacher to understand and communicate their own thinking. The Solutions/Examples parts in this chapter generally only show one way of approaching the task, please note that at times there are several correct processes.
Additional practical information relating to this chapter:
- Prism 333, 444 or 555 refers to a prism built from two Logifaces blocks that has a height of 3, 4 or 5 units.
- We use the notation Cnk for "n choose k", the number of ways to choose an (unordered) subset of k elements from a fixed set of n elements, so Cnk=n!k!(n-k)!.
- Probability of an event:
- By Total number of outcomes we refer to the whole 9 or 16 pcs Logifaces Set, instead of the total 11 different existing Logifaces pieces.
- The addition rule of probability states for two events A and B that
Exercises training Combinatorics skills and about Probability
601 - Matchmaking
602 - Pairing 9pcs
603 - Pairing 16pcs
604 - Variety of Blocks
605 - Stacking Toblerone 9pcs
606 - Stacking Toblerone 16pcs
607 - Block in the Middle
608 - 4 Block Triangles
609 - Hexagon Count
610 - Coloring Vertices 222
611 - Coloring Vertices 133
612 - Coloring Edges 222
613 - Coloring Edges 133
614 - Pick one Block
615 - Pick three Blocks
616 - Pick a Pair
617 - Can you Match them?
618 - Variety with Formulas
619 - Probability of a Given Height
620 - Conditional Probability
621 - Fitting Faces
622 - Addition Rule of Probability
623 - Cutting along Edges
