You are a high school counselor with 9 students who applied for 3 different summer jobs: Job A, Job B, and Job C. Each of the summer jobs has 3 openings apiece, so all 9 students will have a placement. Your responsibility is to place the 9 students with the 9 summer jobs based on the students’ preferences, which are represented in the following chart.

Explain in at least 50 words whether or not providing each student with his/her 1st preference would solve this problem.

We have only 3 B available, and as per the requirement. we need to provide each of them with 1st preference. However, five students have the first preference as B, and we have only 3 B available. Thus, the dream of providing each of them with first preference job seems to be impossible, as we are 2 short of what is required, and that is 5. No combination is possible hence.

Explanation:

Remember we have 9 students, but we have only 3 B available and we have five students with B as first preference. Hence, we are 2 less than the number of B required. No way hence we can provide all the students the job, which is their first preference.