Combinatorics math questionA school is preparing the schedul

(Combinatorics math question)A school is preparing the schedule of classes for the next academic year. They are concerned about scheduling calculus, physics, English, statistics, economics, chemistry, and German classes, planning to oer a single section of each one. Below are the lists of courses that each of six students must take in order to successfully graduate. Determine the smallest number of class periods that can be used to schedule these courses if each student can take at most one course per class period. Explain why fewer class periods cannot be used.

Solution

if select 1 st period chemistry from calculus, physics, English, statistics, economics, chemistry, and German classes then 4 students attend.

and 2 nd period physics from calculus, physics, English, statistics, economics, chemistry, and German classes then 2 students attend.

and 3 rd period english from calculus, physics, English, statistics, economics, chemistry, and German classes then 2 students attend.

and 4 th period economics from calculus, physics, English, statistics, economics, chemistry, and German classes then 2 students attend.

and 5 th period german from calculus, physics, English, statistics, economics, chemistry, and German classes then 2 students attend.

and 6 th period calculas from calculus, physics, English, statistics, economics, chemistry, and German classes then 1 student attend.

and 7 th period statistics from calculus, physics, English, statistics, economics, chemistry, and German classes then 1 student attend.

in one class only one subject can teach.