1. The problem statement, all variables and given/known data Show that if n is a positive integer at most equal to m, then (m n) + (m n-1) = (m+1 n). 2. Relevant equations 3. The attempt at a solution I understand that (m n) = m!/n!(m-n)!. I'm not entirely sure how to figure out (m n-1) because the book I'm studying from never explains this. It merely explains factorials and then shows that (m n) = m!/n!(m-n)!; however, I can at least figure out by reasoning it out that (m n-1) = m!/(m-n+1)!(n-1)!. However, I cannot understand how the next step goes. If we're adding m!/n!(m-n)! and m!/(m-n+1)!(n-1)! then I'm at a loss. The book says that the common denominator is n!(m-n+1)!, but I don't understand that. And the numerator comes out to be m!(m-n+1)+m!n?! This I just cannot understand! I've turned this problem over in my head for over and hour and still nothing! Please help!