Draw a line with 3 distinct points on it. Label each with a different letter. What is the maximum number of different rays that can be named?
3P3 = 3! = 6
To determine the maximum number of different rays that can be named from the three distinct points on the line, we need to consider the combination of the points.
Let's call the three distinct points on the line A, B, and C.
To form a ray, we start at one of the points and extend indefinitely in one direction.
From point A, there are two rays that can be formed: ray AB and ray AC.
From point B, there are also two rays: ray BA and ray BC.
From point C, there are two rays: ray CA and ray CB.
Thus, the maximum number of different rays that can be named from the three distinct points on the line is 6.
To determine the maximum number of different rays that can be named on a line with three distinct points, we need to understand the concept of rays on a line.
A ray is a part of a line that has one endpoint and extends infinitely in one direction. In this case, since we have a line with three distinct points, let's label them as A, B, and C.
To name a ray, we need to specify its endpoint and a different point on the ray. We have three points on the line, so let's consider the possible combinations:
1. Ray starting at A: We can name rays starting at A with the following points as endpoints: B and C, making 2 rays in total (AB and AC).
2. Ray starting at B: We can name rays starting at B with the following points as endpoints: A and C, making 2 rays in total (BA and BC).
3. Ray starting at C: We can name rays starting at C with the following points as endpoints: A and B, making 2 rays in total (CA and CB).
Adding up the total number of rays starting from each point, we have 2 + 2 + 2 = 6 rays.
Therefore, the maximum number of different rays that can be named on a line with three distinct points is 6.