Questions: An election ballot asks voters to select six city commissioners from a group of twenty candidates. In how many ways can this be done

Transcript text: An election ballot asks voters to select six city commissioners from a group of twenty candidates. In how many ways can this be done

Solution

Solution Steps

To determine the number of ways to select six city commissioners from a group of twenty candidates, we need to use the concept of combinations. The formula for combinations is given by:

$C(n, k) = \frac{n!}{k!(n-k)!}$

where $n$ is the total number of candidates, and $k$ is the number of candidates to be selected.

Step 1: Identify the Problem

We need to determine the number of ways to select six city commissioners from a group of twenty candidates. This is a combination problem where we are choosing $k$ items from $n$ items without regard to the order.

Step 2: Use the Combination Formula

The formula for combinations is given by: $C(n, k) = \frac{n!}{k!(n-k)!}$ where $n$ is the total number of candidates, and $k$ is the number of candidates to be selected.