What is the minimum number of points that a candidate can earn in an election using the Borda count method if there are four candidates in 25 voters? Minimum number points, a candidate can earn is ______

To determine the minimum number of points that a candidate can earn in an election using the Borda count method, we need to understand how the method works.

In the Borda count method, each candidate receives points based on their rank in each voter's preference list. The candidate ranked first by a voter receives the highest number of points, the candidate ranked second receives the second-highest number of points, and so on.

In this case, there are four candidates and 25 voters. The maximum number of points a candidate can earn is equal to the sum of the numbers from 1 to the number of candidates. So in this case, it would be the sum of the numbers from 1 to 4.

To find the sum of the numbers from 1 to 4, we can use the formula for the sum of an arithmetic series:

S = \frac{n}{2}(a + L)

where:
- S is the sum of the series,
- n is the number of terms in the series,
- a is the first term, and
- L is the last term.

In this case, n = 4 (number of candidates), a = 1 (first term), and L = 4 (last term). Plugging these values into the formula, we have:

S = \frac{4}{2}(1 + 4) = 10

Therefore, the maximum number of points a candidate can earn using the Borda count method is 10.