The Kangaroo Lodge of Madison Country has 10 members ( A , B , C , D , E , F , G , H , I and J ). The club has five working committees: the Rules Committee ( A , C , D , E , I , and J ), the Public Relations Committee ( B , C , D , H , I and J ), the guest speaker committee ( A , D , E , F , and H ), the New Year’s Eve Party Committee ( D , F , G , H , and I ), and the Fund raising Committee ( B , D , F , H . and J ). a. Suppose we are interested in knowing which pairs of members are on the same committee. Draw a graph that models this problem. ( Hint: Let the vertices of the graph represent the members.) b. Suppose we are interested in knowing which committees have members in common. Draw a graph that models this problem. ( Hint: Let the vertices of the graph represent the committees.)
The Kangaroo Lodge of Madison Country has 10 members ( A , B , C , D , E , F , G , H , I and J ). The club has five working committees: the Rules Committee ( A , C , D , E , I , and J ), the Public Relations Committee ( B , C , D , H , I and J ), the guest speaker committee ( A , D , E , F , and H ), the New Year’s Eve Party Committee ( D , F , G , H , and I ), and the Fund raising Committee ( B , D , F , H . and J ). a. Suppose we are interested in knowing which pairs of members are on the same committee. Draw a graph that models this problem. ( Hint: Let the vertices of the graph represent the members.) b. Suppose we are interested in knowing which committees have members in common. Draw a graph that models this problem. ( Hint: Let the vertices of the graph represent the committees.)
Solution Summary: The author illustrates how to model a situation in which we can find out the pairs of members in the same committee
The Kangaroo Lodge of Madison Country has
10
members (
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
and
J
). The club has five working committees: the Rules Committee (
A
,
C
,
D
,
E
,
I
,
and
J
), the Public Relations Committee (
B
,
C
,
D
,
H
,
I
and
J
), the guest speaker committee (
A
,
D
,
E
,
F
,
and
H
), the New Year’s Eve Party Committee (
D
,
F
,
G
,
H
,
and
I
), and the Fund raising Committee (
B
,
D
,
F
,
H
.
and
J
).
a. Suppose we are interested in knowing which pairs of members are on the same committee. Draw a graph that models this problem. (Hint: Let the vertices of the graph represent the members.)
b. Suppose we are interested in knowing which committees have members in common. Draw a graph that models this problem. (Hint: Let the vertices of the graph represent the committees.)
A corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief
financial officer (CFO). It must also appoint a planning committee with three different members. There are 16 qualified
candidates, and officers can also serve on the committee. Complete parts (a) through (c) below.
a. How many different ways can the officers be appointed?
There are
different ways to appoint the officers.
b. How many
different ways can the committee be appointed?
There are
different ways to appoint the committee.
c. What is the probability of randomly selecting the committee members and getting the three youngest of the
qualified candidates?
P(getting the three youngest of the qualified candidates) =
(Type an integer or a simplified fraction.)
A corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It must also appoint a planning
committee with three different members. There are 11 qualified candidates, and officers can also serve on the committee. Complete parts (a) through (c) below.
C
a. How many different ways can the officers be appointed?
There are
different ways to appoint the officers.
b. How many different ways can the committee be appointed?
There are
different ways to appoint the committee.
c. What is the probability of randomly selecting the committee members and getting the three youngest of the qualified candidates?
P(getting the three youngest of the qualified candidates) =
(Type an integer or a simplified fraction.)
A corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It must also appoint a planning committee with three different members. There are 13 qualified candidates, and officers can also serve on the committee. Complete parts (a) through (c) below.
a. How many different ways can the officers be appointed?
There are different ways to appoint the officers.
b. How many different ways can the committee be appointed?
There are different ways to appoint the committee.
c. What is the probability of randomly selecting the committee members and getting the three youngest of the qualified candidates
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