AI & ML · Probability for ML

Counting & combinatorics

78 problems in this skill, each with a solver-verified answer key. Answers are checked the moment you submit — with a hint if you want one and a worked solution afterwards.

What the problems look like

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

Warm-up
A dataset has $7$ candidate features. How many distinct subsets of exactly $3$ features can you select for a model, if order does not matter? That is, compute $\dbinom{n}{r}$ for $n = 7$ , $r = 3$ .
Warm-up
A dataset has $8$ candidate features. How many distinct subsets of exactly $5$ features can you select for a model, if order does not matter? That is, compute $\dbinom{n}{r}$ for $n = 8$ , $r = 5$ .
Warm-up
A dataset has $11$ candidate features. How many distinct subsets of exactly $2$ features can you select for a model, if order does not matter? That is, compute $\dbinom{n}{r}$ for $n = 11$ , $r = 2$ .

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

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