As all the students are equally brilliant in the game, so we can say that all the elements of our universe are homogeneous and identical. In this regard, all the students deserve a fair and equal chance of being selected into the team. Therefore, random sampling technique (lottery method), being a scientific method and free from any personal bias, would be the most appropriate to use for the selection of students.
Process of selection: First of all, write the name of each student on identical (in terms of size, colour, etc) slips of paper (total 10 slips). Now, place all the slips in a box or a container and shuffle well. After this draw one by one 3 slips from the box. Students with their name on the drawn slips would be selected for the tournament.