Eight points are marked on a circle, no three of them in a straight line. How many different triangles can be drawn whose three corners are all marked points?

A triangle is settled the moment you name its three corners, and the order in which you name them does not matter. Choosing three points in order can be done in $8\times 7\times 6=336$ ways, but each set of three points has been counted once for every ordering of those three, and three things can be ordered in 6 ways. So the count is 336 ÷ 6 = 56. The traps: 336 stops before dividing and so counts each triangle six times over; 168 divides by 2 instead of 6, the correction that suits pairs rather than triples; 24 is $8\times 3$, multiplying the number of points by the number of corners.