Rules of sum and product, Pₙ, Aₙᵏ and Cₙᵏ
Tell the rule of sum from the rule of product, use the textbook formulas for permutations, arrangements and combinations, and solve an equation with factorials.
- Ukraine: grade 11
- Russia: grade 9
Guide
This follows Ukrainian Grade 11 algebra §12–13. «Or» adds the numbers of ways, «and» multiplies them. Pₙ = n!, Aₙᵏ = n! : (n − k)! (order matters), Cₙᵏ = n! : (k! (n − k)!) (order does not matter).
Common slips: multiplying where you should add, allowing repeats, forgetting to divide by k!, and mixing arrangements with combinations.