组合数学 (Fall 2017)/Problem Set 1

Problem 1

Find the number of ways to select [math]\displaystyle{ 2n }[/math] balls from [math]\displaystyle{ n }[/math] identical blue balls, [math]\displaystyle{ n }[/math] identical red balls and [math]\displaystyle{ n }[/math] identical green balls.

• Give a combinatorial proof for the problem.
• Give an algebraic proof for the problem.