Three teachers in an elementary school must decide in which of three classrooms they wil...

Three teachers in an elementary school must decide in which of three classrooms they will each teach. The teachers will use the method of points to make the decision. The teachers each divide 100 points among the three rooms, and their point assignments are listed in the following table.

a. List the six possible arrangements of teachers to rooms, and identify the smallest point value assigned to a room in each case.

b. How many arrangements are there for which the smallest number is as large as possible?

c. How should the rooms be assigned to the teachers?