Nine students are split into three equal teams to develop reports on one of three problems: shortage of skilled labor, violence in schools, and low standardized test scores. If each team will report on a different problem, then how many different assignments of students to problems are possible?

Answer Choices

Correct answer marked below

5040

1680

Correct

1512

504

168

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Explanation

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Official Explanation

Official

Problem I = shortage of skilled labor; Problem II = violence in schools; Problem III = low standardized test scores

Since 3 equal teams are formed from 9 students, number of students in each team = 3.

Number of ways in which 3 (out of 9) students can be chosen for Problem I =

\binom{9}{3}

Number of ways in which 3 (out of remaining 6) students can be chosen for Problem II =

\binom{6}{3}

…

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What this question tests

What it tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Common trap

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.