Discrete Mathematics

226

DISCRETE

MATHEMATICS'--------------------------

intersection point

of

two lines, then we see that four regions meet at this point, and the point is the lowest point

of

exactly one

of

them.

Thus, the number

of

lowest points is the same as the number

of

intersection points

of

the lines, plus the

number

of

intersection points between lines and the lower edge

of

the blackboard, plus one. Since any two

lines intersect, and these intersection points are all different (this is where we use the lines being in general

position), the number

of

such lowest points is

(~)+

n

+I.

7.3

COUNTING SUBSETS

7.3.1

The

Number

of

Ordered Subsets

At

a competition ...