An election ballot asks voters to select three city judges from a group of 12 candidates. How many ways can this be done?



Answer to a math question An election ballot asks voters to select three city judges from a group of 12 candidates. How many ways can this be done?

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This problem involves combinations, as the order in which the judges are selected does not matter. The formula for combinations is given by: \[ C(n, k) = \frac{n!}{k!(n-k)!} \] where \(n!\) denotes the factorial of \(n\), which is the product of all positive integers up to \(n\). In this case, there are 12 candidates, and voters need to select 3 judges. Therefore, the number of ways to select 3 judges from a group of 12 candidates is given by: \[ C(12, 3) = \frac{12!}{3!(12-3)!} \] Let's calculate this: \[ C(12, 3) = \frac{12!}{3! \cdot 9!} \] \[ C(12, 3) = \frac{12 \cdot 11 \cdot 10}{3 \cdot 2 \cdot 1} \] \[ C(12, 3) = 220 \] So, there are 220 ways to select three city judges from a group of 12 candidates.

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