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Combinations (Easy)

AMC 10 Q1–8 depth — contest entry, not school drills.

Easy Medium Hard AIME / USAJMO / AMO

Combinations: core idea

\binom nk

.

Example problem: hint and answer

How many ways can $2$ students be chosen from $5$ ?

Hint: Selections ignore order: use $\binom nk$ . Answer: 10.

Practice (9 problems — type your answers)

1. How many $3$ -element subsets does a $6$ -element set have?
2. How many ways can a committee of $1$ be selected from $8$ people?
3. How many diagonals does a pentagon have?
4. How many ways can $4$ toppings be chosen from $7$ ?
5. How many pairs can be formed from $9$ people?
6. How many ways can $3$ cards be chosen from $5$ cards?
7. How many subsets of size $0$ does any set have?
8. How many triangles are determined by $6$ points with no three collinear?
9. How many ways can $2$ flavors be chosen from $4$ ?

Combinations Practice Problems — Easy