8.1. In a class, there are 30 students. Each student has a single-colored t-shirt and single-colored pants. Both the t-shirts and the pants come in exactly 15 different colors. Will there always be 15 students such that any two of them have t-shirts of different colors and pants of different colors?
Answer: Not always.

Solution: An example can be constructed where even three students satisfying the condition cannot be found. Let 15 students have shirts of different colors and pants of the same color, while the remaining 15 students have pants of different colors (including the color of the pants of the first 15 students) and shirts of the same color (this color also appeared among the shirts of the first 15 students). Then, among any three students, two will either be from the group with shirts of different colors or from the group with pants of different colors, but then these two will have either pants or shirts of the same color.