1. Objective / Мета роботи #

Gain fluency in counting the outcomes of a choice — arrangements, combinations, and multisets — and in turning those counts into probabilities of everyday random experiments.

By the end of the class the student should be able to:

• apply the product rule to a choice made in stages (car plates, lottery cards) and recognise when repetition is allowed ($n^k$) or not;
• tell order-matters from order-ignored problems and pick the right formula — an arrangement $P(n,k)=\dfrac{n!}{(n-k)!}$ when order matters, a combination $C(n,k)=\dbinom{n}{k}$ when it does not;
• count distributions of identical objects into distinct boxes with the multiset (stars-and-bars) formula $C(n{+}k{-}1,\,k)$;
• compute a classical probability as favourable outcomes over total, and combine events with the product rule for independent trials, the conditional rule when one event constrains another, and the complement rule $P(A)=1-P(\overline A)$ for “at least one”;
• model an urn/selection problem from words to a formula, and give the answer as an exact fraction and a decimal.

The class consolidates Lecture 13 — Probabilities (combinatorics and the classical definition, conditional probability, and independence) and complements Lab 7. All theory needed is restated, self-contained, in 2method.md.

Practical/Practical6/1purpose.md · 1.5 KB · updated 2026-07-31 21:14