Question

There are 2 red, 5 green, 3 blue, and 4 white points on a circle. Find the number of line segments which have vertices of different colors at the given points.

Answer 1

Each line segment from a red point that goes to either a green point or a blue point has endpoints of different colors.
There are 7 segments from each red point and there are 5 red points, for a total of 35 segments.

Each line segment from a green point that goes to either a red point or a blue point has endpoints of different colors.
There are 8 segments from each green point and there are 4 green points, for a total of 32 segments.

Each line segment from a blue point that goes to either a green point or a red point has endpoints of different colors.
There are 9 segments from each blue point and there are 5 blue points, for a total of 27 segments.

Adding these together, we get 35 + 32+ 27 = 94 segments.
However, we have counted each segment twice, so we need to divide that answer by 2: 47 segments.

Answer 2

Explanation:

The number of those line segments which have endpoints of different colors is 47.

What is permutation and combination?

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

We have:

There are 5 red, 4 green, and 3 blue points on a circle.

There are different colored endpoints on each line segment that starts at a red point and travels to either a green point or a blue point.

There are 5 red points and 7 segments from each of them, making a total of 35 segments.

There are different colored endpoints on each line segment that leaves at a green point and travels to either a red or blue point.

There are 4 green points and 8 segments from each, for a total of 32 segments.

There are different colored endpoints on each line segment that leaves at a blue point and travels to either a green point or a red point.

Each blue point has 9 segments, and there are a total of 5 blue points.

Add all the ways = 35 + 32+ 27

= 94 segments.

Number of segment = 94/2 = 47

Thus, the number of those line segments which have endpoints of different colors is 47.