The student governing board at Milton University consists of 7 members: Andy, Bi

Question

The student governing board at Milton University consists of 7 members: Andy, Bill, Cathy, David, Evelyn, Frank, Gina. list and count the different ways of electing each of the following:

. A president and secretary if one person can hold both offices.

.A president and a secretary if the president must be a female.

.A president and secretary if the two officers must not be the same sex.

.A president, a secretary and a treasurer.

.A president, a secretary, and a treasurer, if the president must be a man and the other two must be women.

.A president, a secretary, and a treasurer, if the secretary must be a woman and the other two must be men.

PLEASE EXPLAIN YOUR ANSWERS AND SHOW ALL THE WORK.

Explanation / Answer

Male: Bill (B), David (D), Frank (F), Andy (A)

Female: Cathy (C), Evelyn (E), Gina (G)

A president and secretary if one person can hold both offices:

For president we have 7 choices and for secretary we also have 7 choices so possible ways of selecting president and secretary is 7*7 = 49. Following is the possible list:

--------------------------

A president and a secretary if the president must be a female:

That is president must be female and seceratry can be male or female.

President can be choosed in 3 ways and seceratry in 7 ways. So possible number of ways, assuming one person can hold both offcies, is 7*3=21

Following table shows the list:

---------------------------------------------------

A president and secretary if the two officers must not be the same sex:

When president is female and seceratry is male then possible number of ways is 4*3 =12

When president is male and seceratry is female then possible number of ways is 3*4 =12

So total possible ways is 12+12=24 ways

Following is the possible list:

----------------------

Assuming one person can hold only one office so the possible number of ways of selecting a president, a secretary and a treasurer is 7*6*5= 210

Here if we consider ABC, ACB, BAC, BCA, CAB, CBA same then possible number of selections is 210/6 = 35.

President Seceratry A A A B A C A D A E A F A G B A B B B C B D B E B F B G C A C B C C C D C E C F C G D A D B D C D D D E D F D G E A E B E C E D E E E F E G G A G B G C G D G E G F G G

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.