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Counting Without Listing: Probability & Statistics: Uncharted

Courses Probability & StatisticsCounting Without Listing

Counting Without Listing

Count huge outcome spaces by reading their structure: stages, ordered roles, unordered groups, and complements.

Probability & Statistics
Unit 3 of 12
20 lessons
154 min
420 XP

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Lessons

20 total

1Too Many to ListRecognize staged choices as a product instead of an ever-growing list.InteractiveConcept7 min20 XPOpen
2The Multiplication PrincipleMultiply the number of options across independent stages.InteractiveConcept7 min20 XPOpen
3Three StagesCount codes when choices may repeat from one slot to the next.InteractiveConcept7 min20 XPOpen
4Slots That ShrinkCount ordered selections when an option cannot be reused.InteractiveConcept7 min20 XPOpen
5The FactorialInterpret factorial notation as a descending product of positive integers.InteractiveConcept7 min20 XPOpen
6Principle WorkoutChoose and evaluate products for staged counting situations.InteractivePractice9 min20 XPOpen
7Order Matters, or NotSeparate ordered arrangements from unordered selections.InteractiveConcept7 min20 XPOpen
8Teams, Not LineupsCorrect an ordered pair count when only the selected team matters.InteractiveConcept7 min20 XPOpen
9Divide Out the OrderCompute a combination by dividing permutations by internal arrangements.InteractiveConcept8 min20 XPOpen
10Pascal's ShortcutBuild a row of Pascal's triangle by adding adjacent entries above it.InteractiveConcept8 min20 XPOpen
11Count Then ChanceUse combinations to count favorable and total hands before forming a probability.InteractiveConcept8 min20 XPOpen
12The Birthday SurpriseUse a complement product to reason about at least one shared birthday.InteractiveConcept8 min20 XPOpen
13Arrangements WorkoutCount fresh ordered arrangements with shrinking slots and factorials.InteractivePractice9 min20 XPOpen
14Handshakes and EdgesRecognize pair counting as a two-item combination.InteractiveConcept7 min20 XPOpen
15Paths on a GridConnect shortest grid routes with choosing positions for repeated moves.InteractiveConcept8 min20 XPOpen
16Lottery ArithmeticCount a lottery outcome space honestly with combinations.InteractiveConcept8 min20 XPOpen
17With or Without ReplacementIdentify when replacement keeps or shrinks later-stage counts.InteractiveConcept7 min20 XPOpen
18Counting WorkoutDistinguish products, permutations, and combinations in mixed cases.InteractivePractice9 min20 XPOpen
19Choose Your CounterMatch a scenario to the counting tool that fits its structure.InteractiveConcept7 min20 XPOpen
20Counting Mastery CheckCombine selection, ordering, and staged choices in one count.InteractiveMastery check9 min40 XPOpen

Describing Data When One Thing Changes Another