1. The problem statement, all variables and given/known data Let n be an element of the positive numbers (Z+). Prove that 3 divides (3n n) or "3n choose n". Use the definition of a binomial coefficient to solve. 2. Relevant equations Definition of a Binomial Coefficient: (n k) := ( n! / k!(n - k)! ) 3. The attempt at a solution I've done the basics. I've replaced n and k with 3n and n, making the equation: (3n n) = ( 3n! / n!(3n - n)! ), then simplifying to ( 3n! / n!(2n)! ), which equals just ( 3 / 2n! ). If it is divisible by 3, I suppose this can be expressed as: (( 3 / 2n! )) / 3 = k, and therefore, ( 3 / 2n! ) = 3k . It seems like the real proof here is in showing that 2n! is an integer. How do I go forward?