Probability and combinations
Find the probability of an event with P(A) = m : n when the outcomes of a choice are counted with combinations Cₙᵏ and arrangements Aₙᵏ.
- Ukraine: grade 11
Guide
Topic from the Ukrainian Grade 11 textbook (algebra and calculus with geometry), section 3 "Elements of combinatorics, probability and statistics", item 14 "The classical definition of the probability of a random event". When all outcomes of an experiment are equally likely, P(A) = m : n, where n is the number of all possible outcomes and m the number of outcomes favourable to A.
When k of n objects are chosen at random and the order does not matter, n = Cₙᵏ = n! : ((n − k)! · k!). When objects are chosen from two groups at once, the number of favourable outcomes m is the product of the numbers of ways to choose from each group. When the order matters (a number with different digits), use arrangements Aₙᵏ = n! : (n − k)!. Solutions are laid out as in the book: "Given", "Find", "Solution", "Answer". The answer is a fraction in lowest terms.
The textbook example (problem 3): of 28 apples, 15 are yellow and 3 apples are chosen; P = C₁₅³ : C₂₈³ = 5 : 36.