Exercise 437Combinatorics › Counting principlesHigh schoolAdded 3 Nov 2026

Arrangements

#arrangements#ordered selection#permutations

Statement

From $10$ students, how many ways can we select a president, a vice-president, and a treasurer (all distinct)?

Hint

Order matters: $A_{10}^3=10\cdot9\cdot8$ .

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Choices. President: $10$ choices; then VP: $9$ ; treasurer: $8$ .

Product. $10\cdot9\cdot8=720$ .

Conclusion. There are $720$ ordered selections.

Formula. $A_n^k=\frac{n!}{(n-k)!}$ .