permutations

Convert the statement to:

\binom{n}{r} + \binom{n}{r-1}=\binom{n+1}{r}

Now, think of the this situation:

You have n+1 players out of which one player has a slight niggle. You have to form a team of r players. LHS represents the no. of ways of forming the team, where you take the r players from the n fit players or take the slightly injured player and choose the remaining r-1 players from the fit n players.

Now, RHS also says the same thing.. We want to choose r players from a set of n+1 players. Hence, proved :)