Problem

Is this work overcounting or undercounting? using \(10P_{3}\) for a \(3\text{-}\text{person}\) committee

Big Picture

What this problem is really about

To diagnose a counting error, compare what the formula treats as distinct with what the situation treats as distinct. We’ll interpret the permutation’s ordered positions, test whether a plain committee has such roles, measure how many listings represent one membership group, and compare with the combination count.

Answer choices

Choose your path.

Preview only

This work is overcounting because 10P3 treats different orders of the same 3 people as different committees.

This work is overcounting because some committees repeat the same type of person, so 10P3 counts identical choices more than once.

This work is undercounting because 10P3 only chooses 3 people and does not include every possible committee.

This work is undercounting because a committee has 3 different spots, so the order should matter for who is chosen first, second, and third.

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

Is this work overcounting or undercounting? using \(10P_{3}\) for a \(3\text{-}\text{person}\) committee

What this problem is really about

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.