MATH U113 · Counting drill · §2.3 (self-study)

Counting Drill

Six counting problems per sheet, in the exact styles of the course's Tutorial 1: identical-item arrangements, labelled groups, the glue trick, constrained committees, and counting-based probability. A fresh randomized sheet every visit.

Why this drill exists

The handout marks counting (§2.3) self-study — no lecture covers it, for anyone. The tutorial sheet then uses patterns beyond Devore's section (multinomial arrangements, group splits). The Module 1 lesson, section 3 teaches every pattern here from zero; this page turns that understanding into speed.

How to drill

Work on paper, timed. First decision on every problem, written in words before any arithmetic: ordered or unordered? any identical copies? any constraint? Then compute. Reveal, mark yourself, and for any miss open "see the method" and find the exact step that broke. Under 12 minutes with all six right is fluent; one sheet a day for a week closes the §2.3 gap for good.

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This sheet's six