Question 100
We write $99$ circles in a line and in their interior we write the numbers from $1$ to $99$, as follows:
We color each circle with one of the two colors: red (R) and green (G). We say that a coloring is «good», if the following happens:
The number of red circles in the first part of numbers from $1$ to $50$ is greater than the number of the red circles existing in the second part from number $51$ to $99$.
a. Determine how many different colorings can be constructed.
b. Determine how many different “good” colorings can be constructed.
(Note: Two colorings are different, if they have different colors at least in one circle.)
We color each circle with one of the two colors: red (R) and green (G). We say that a coloring is «good», if the following happens:
The number of red circles in the first part of numbers from $1$ to $50$ is greater than the number of the red circles existing in the second part from number $51$ to $99$.
a. Determine how many different colorings can be constructed.
b. Determine how many different “good” colorings can be constructed.
(Note: Two colorings are different, if they have different colors at least in one circle.)