A club has 35 members of which 5 are computer systems majors, 10 are accounting
ID: 3174761 • Letter: A
Question
A club has 35 members of which 5 are computer systems majors, 10 are accounting majors, 7 are management majors and 13 are marketing majors. How many committees committees of 4 people can be formed: 1. if all members are to have different majors. 2. if there must be at most 2 accounting majors. 3. if a marketing marketing major must be the chair. 4. if one member is the chair and another the recorder. 5. If there must be at least one management major. A club has 35 members of which 5 are computer systems majors, 10 are accounting majors, 7 are management majors and 13 are marketing majors. How many committees committees of 4 people can be formed: 1. if all members are to have different majors. 2. if there must be at most 2 accounting majors. 3. if a marketing marketing major must be the chair. 4. if one member is the chair and another the recorder. 5. If there must be at least one management major.Explanation / Answer
Case 1: if all members are to have different majors.
Solution : If all members are from different majors then the possible number of different committees would be ,
N = 5*10*7*13 = 4,550
Case 2 : if there must be at most 2 accounting majors.
Solution : If there have to be at most 2 accounting majors then we will divide this scenario into 3 cases where the first case would have 2 accounting majors fixed and the rest 2 can be taken from the pool of rest of 25 majors. SImilarly next case will be when we will fix one accounting major and the rest 3 members can be selected from the pool of rest 25 majors. Last case will be when there will be no accounting major and all majors will be selected from the pool of 25 majors. Therefore the number of committees would be given by,
N = C(10,2)*C(25,2)+C(10,1)*C(25,3)+C(25,4) = 49,150
Case 3 : if a marketing marketing major must be the chair.
Solution : In this case we will fix the chair position to a marketing manager and the rest of the 3 positions can go to any of the rest 34 majors. Therefore the number of committees would be given by,
N = C(13,1)*C(34,3) = 77,792
Case 4 : if one member is the chair and another the recorder.
Solution : Here there are 2 different posts and rest of the posts are identical. Thus the number of committees would be given by,
N = C(35,1)*C(34,1)*C(33,2)= 628,320
Case 5 : If there must be at least one management major.
Solution : For this case we can find the number of committes where there are no management majors and substract them from the total number of committees that can be formed.
N = C(35,4) - C(28,4) = 31,885
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