22 Given a group of students GAllen Brenda Chad Dorothy Eric

22. 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. A treasurer and a secretary if two must not be the same sex.

A) 6       B) 12             C) 3        D) 10

23. Find the probability. If 81% of scheduled fights actually take place and cancellations are independent events, what is the probability that 3 separate flights will all take place?

A) 0.81          B) 0.53          C) 0.01          D) 0.66

Solution

22.

In the Group G={A, B, C, D, E}, the male ones are {A, C and E} and the female ones are {B, and D}.

Since the number of cases are very small here I will write all the possible cases of selecting a secretary and a treasurer given that both posts should contain people from different sex.

Secretary

Treasurer

A

B

A

D

C

B

C

D

E

B

E

D

B

A

B

C

B

E

D

A

D

C

D

E

Since there are a total of 12 possible cases , B is the correct option.

23.

Assuming each flight is independent of each other,

P(3 flights takes place ) = 0.81*0.81*0.81 = 0.53

Thus option B is correct.