Question

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

285

likes1425 views

Corbin

4.6

57 Answers

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.

Frequently asked questions (FAQs)

What are the key features of the graph of the logarithmic function f(x) = log(base 2)(x+2)?

+

What is the variance of the numbers 4, 7, 9, 12, and 15?

+

What is the relationship between the interior angles of two congruent triangles?

+

New questions in Mathematics