Probability and Statistics - Probability with Factorials Practice

This math unit advances students' understanding of probability, permutations, and combinations through a series of incremental and integrated topics, focusing heavily on factorial notation and applications in real-world contexts. It starts with an exploration of factorial multiplication, moves on to describing the transformation of factorial expressions into binomial coefficients (nCm notation), and then applies these principles to practical situations. The unit progresses from calculating factorial expressions for ordering a small number of items with no repetitions to more complex scenarios involving ordering larger sets and considering repetitions. As it progresses, students tackle increasing complexities in arranging items and translating these arrangements into factorial equations and multiplicative expressions. Later in the unit, there is an introduction to calculating probabilities of drawing cards, emphasizing combinatorial calculations and the formulation of probabilities as equations and fractions. Overall, this unit builds a robust understanding of probability, factorial calculations, and their applications in different statistical scenarios.