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Question : Three representatives if two must be male and one must be female : 2151690

**MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.**

**Given a group of students: G = {Allen, Brenda, Chad, Dorothy, Eric} or G = {A, B, C, D, E}, count the different ways of choosing the following officers or representatives for student congress. Assume that no one can hold more than one office.**

1) Three representatives, if two must be male and one must be female

A) 6

B) 12

C) 4

D) 2

2) Four representatives

A) 10

B) 1

C) 120

D) 4

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

A) 4

B) 12

C) 3

D) 6

4) Three representatives, if two must be female and one must be male

A) 2

B) 5

C) 6

D) 3

5) A treasurer and a secretary if the two must not be the same sex

A) 3

B) 12

C) 10

D) 6

6) A male president and three representatives

A) 72

B) 9

C) 3

D) 6

**Four accounting majors, two economics majors, and three marketing majors have interviewed for five different positions with a large company. Use the following information to find the number of different ways that five of these could be hired.**

7) There is no restriction on the college majors hired for the five positions.

A) 120 ways

B) 15,120 ways

C) 3024 ways

D) 24 ways

8) Two accounting majors must be hired first, then one economics major, then two marketing majors.

A) 4 ways

B) 288 ways

C) 24 ways

D) 144 ways

9) Instead of five positions, the company has decided that only three different positions, with no restriction on the college majors, must be filled.

A) 6 ways

B) 2520 ways

C) 504 ways

D) 24 ways

10) The four accounting majors must be hired first, and then the final position would be chosen from the remaining majors.

A) 100 ways

B) 2880 ways

C) 120 ways

D) 480 ways

11) One accounting major, one economics major, and one marketing major would be hired, then the two remaining positions would be filled by any of the majors left.

A) 48 ways

B) 4320 ways

C) 2160 ways

D) 720 ways

**An order of award presentations has been devised for seven people: Jeff, Karen, Lyle, Maria, Norm, Olivia, and Paul.**

12) In how many ways can the people be presented?

A) 49

B) 720

C) 2520

D) 5040

13) In how many ways can the awards be presented so that Maria and Olivia will be next to each other?

A) 720

B) 1220

C) 1680

D) 1440

14) In how many ways can the men be presented first and then the women?

A) 72

B) 144

C) 5040

D) 2

15) In how many ways can the first award be presented to Karen and the last to Lyle?

A) 120

B) 360

C) 840

D) 24

16) In how many ways can the awards alternate between men and women with the first award being presented to a woman?

A) 12

B) 144

C) 1008

D) 72

**Suppose a traveler wanted to visit a museum, an art gallery, and the state capitol building. 45-minute tours are offered at each attraction hourly from 10 a.m. through 3 p.m. (6 different hours). Solve the problem, disregarding travel time.**

17) In how many ways can the traveler visit all three places in one day?

A) 60

B) 15

C) 30

D) 120

18) In how many ways could the traveler schedule two of the three tours in one day?

A) 30

B) 36

C) 120

D) 180

19) In how many ways could the traveler schedule all three tours in one day, with the museum tour being after noon?

A) 30

B) 20

C) 40

D) 60

20) In how many ways could the traveler schedule all three tours before 1 p.m.?

A) 6

B) 1

C) 3

D) 9

21) In how many ways could the traveler schedule all three tours in one day, with the art gallery being the last tour of the day?

A) 40

B) 60

C) 10

D) 30

**To win the World Series, a baseball team must win 4 games out of a maximum of 7 games. To solve the problem, list the possible arrangements of losses and wins.**

22) How many ways are there of winning the World Series in exactly 7 games if the winning team loses the first game?

A) 8 ways

B) 15 ways

C) 10 ways

D) 6 ways

23) How many ways are there of winning the World Series in exactly 7 games if the winning team wins the first game?

A) 8 ways

B) 10 ways

C) 12 ways

D) 20 ways

24) How many ways are there of winning the World Series in exactly 7 games if the winning team loses the first two games?

A) 5 ways

B) 4 ways

C) 3 ways

D) 2 ways

25) How many ways are there of winning the World Series in exactly 7 games if the winning team wins the first two games?

A) 3 ways

B) 5 ways

C) 4 ways

D) 10 ways

26) How many ways are there of winning the World Series in exactly 7 games if the winning team wins the last two games?

A) 12 ways

B) 8 ways

C) 20 ways

D) 10 ways

27) How many ways are there of winning the World Series in exactly 7 games if the winning team wins the last 3 games?

A) 3 ways

B) 10 ways

C) 5 ways

D) 4 ways

28) How many ways are there of winning the World Series in exactly 6 games if the winning team wins the first game?

A) 3 ways

B) 4 ways

C) 6 ways

D) 5 ways

29) How many ways are there of winning the World Series in exactly 6 games if the winning team loses the first game?

A) 5 ways

B) 7 ways

C) 4 ways

D) 6 ways

30) How many ways are there of winning the World Series in exactly 6 games if the winning team wins the first two games?

A) 3 ways

B) 6 ways

C) 2 ways

D) 4 ways

31) How many ways are there of winning the World Series in exactly 6 games if the winning team wins the last two games?

A) 4 ways

B) 6 ways

C) 3 ways

D) 2 ways