The problem is as follows:
In a line segment, $100$ points are marked as indicated in the figure as shown below, which are numbered consecutively, starting at one end, with the numbers from $1$ to $100$. The points which its corresponding numbers are divisible by $3$ are painted red and the rest blue, how many segments whose ends are of different color the most?
The alternatives given are:
$\begin{array}{ll} 1.&\textrm{2275}\\ 2.&\textrm{2244}\\ 3.&\textrm{2211}\\ 4.&\textrm{2040}\\ \end{array}$
How exactly can I find the number of segments?.
Between $1$ and $100$ the number of points which will have multiples of $3$ be:
$\frac{99-3}{3}+1=33$
Then there will be $33$ points which will be divisible by $3$.
But in $100$ points there will be $99$ segments. But I don't know exactly how can this be scaled to any of those alternatives. Can someone help me?.
You have $33$ red points and $67$ blue points. To make a segment with different colored ends you select one red point and one blue point, which you can do in (how many) ways.