## Task A-1.5. (4 points)

In a bag, there is a sufficiently large number of red, white, and blue balls. Each student randomly takes three balls from the bag. How many students must there be at a minimum to ensure that at least one pair of them has the same combination of balls, i.e., the same number of balls of each color?
## Solution.

Let's denote the red ball with the letter $C$, the white ball with the letter $B$, and the blue ball with the letter $P$. The possible combinations of three balls are:

$C C C, B B B, P P P, C B B, C P P, B C C, B P P, P C C, P B B, C B P$.

There are a total of 10 possible combinations.

(2 points)

To ensure that there are at least two students with the same combination, it is sufficient to have at least 11 students.

(2 points)

Note. The conclusion that for $k$ combinations, $k+1$ students are needed is worth 2 points.