Problem - 2525
Team MAS won a total of $10$ gold medals in a $6$-day tournament. It won at least one gold medal every day. How many different possibilities are there to count the number of gold medals won each day?
Answer
128
This is the same as to count the number of positive integer solutions to $x_1+x_2+x_3+x_4+x_5+x_6=10$. Therefore the answer is $$C_{10-1}^{6-1}=\boxed{126}$$