Counting

Question

Suppose that there are nine students in a discrete mathematics class at a small
college.
a) Show that the class must have at least five male students or at least five female
students.
b) Show that the class must have at least three male students or at least seven female
students.

Comments

Let there are male and female students in the class.

 

Total possible values: 

Male	0	1	2	3	4	5	6	7	8	9
Female	9	8	7	6	5	4	3	2	1	0

 

a) in class there must be atleast 5 male students... it covers following possible values :

Male	5	6	7	8	9
Female	4	3	2	1	0

to cover remaining following possible values from the original set:

Male	0	1	2	3	4
Female	9	8	7	6	5

there should be atleast 5 female students in the class.

 

Therefore the class must have at least five male students or at least five female students.

 

Part B - I hope you can prove.