Mrs Teacher is selecting a group of students to help her gra

Mrs. Teacher is selecting a group of students to help her grade the exams. She needs a coordinator, a grade recorder, 3 graders for the multiple choice, and 5 graders for the work- out problems. The coordinator and grade recorder must be selected from 7 graduate students. The graders must be selected from 13 undergraduate students. (NOTE: Each student can only hold one position and graders cannot grade both multiple choice and work-out problems.) In how many ways can Mrs. Teacher select her helpers?

Solution

One important thing to notice here is that the event of selecting (cordinator and a grade recorder) and 8 graders are independent events since they have to be chosen from different sets of people. So what we will do is find their number of ways seperately and then multiply them to get the required values.

Number of ways of choosing a coordinator and a grade recorder out of 7 graduate students) = C(7,2)*2! = 42

Number of ways of choosing 3graders for multiple choice and 5 graders for work-out problems out of 13 students = 13!/(3!*5!*5!) =72072

Total number of ways = 42*72072 = 3,027,024