Problem preview

S-CP.9 Warmup M2-071-A13-V04

Use permutations and combinations to compute probabilities of compound events and solve problems.

Decide whether a counting setup overcounts or undercounts

Problem

A student wants to count the number of different \(4\text{-}\text{letter}\) arrangements of the letters in TOOT. They use \(4!\). Is this work overcounting or undercounting?

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This work is undercounting because the 4 positions are different roles, so 4! is not enough to count every arrangement.

This work is overcounting because arrangements of letters should be counted like a committee, where order does not matter.

This work is overcounting because 4! treats the two O’s and the two T’s as different, even though swapping identical letters does not make a new arrangement.

This work is undercounting because 4! does not include all the ways the two O’s and two T’s can be arranged in the 4 positions.

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Curriculum context

Course: Math II
Standard: S-CP.9
Category: Statistics and Probability
Domain: Conditional Probability and the Rules of Probability
Objective: Use permutations and combinations to compute probabilities of compound events and solve problems.
Problem type: Decide whether a counting setup overcounts or undercounts