Suppose there are nine students in a discrete mathmatics cla

Suppose there are nine students in a discrete mathmatics class at a small college.

a) Show that the class must have at least 5 male students or at least 5 female students.

b) Show that the class must have at least 3 male students or at least 7 female students.

Please explain

Solution

(a) On assuming that the class only has 4 male students and 4 female students. Total students only equal to 8.

There are 9 students in the class . Therefore there must be at least 5 male students or 5 female students.

(b) On assuming that the class only has 2 male students and 6 female students . Again total students only equal 8.

Therfore there must be atleast 3 male students or 7 female students.