Counting & combinatorics

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   From a class of 8 students, a teacher chooses 3 students to represent the class at the state science fair. The order in which they are chosen does not matter. How many different groups of 3 students are possible? (This count is the number of combinations $C(8, 3)$.)

2. Warm-up

   From a class of 12 students, a teacher chooses 2 students to represent the class at the state science fair. The order in which they are chosen does not matter. How many different groups of 2 students are possible? (This count is the number of combinations $C(12, 2)$.)

3. Warm-up

   From a class of 11 students, a teacher chooses 2 students to represent the class at the state science fair. The order in which they are chosen does not matter. How many different groups of 2 students are possible? (This count is the number of combinations $C(11, 2)$.)

Problems shown under their original terms: Generated (template, solver-computed).