How many ways are there to select a committee of 17 politicians chosen from a room...

How many ways are there to select a committee of 17 politicians chosen from a room full of indistinguishable Democrats, indistinguishable Republicans, and indistinguishable Independents if every party must have at least two members on the committee? If, in addition, no group may have a majority of the committee members?

Solutions

Expert Solution

Answer:

Given that:

To select a committee of 17 politicians chosen from a room full of indistinguishable Democrats, indistiguishable Republicans, and indistinguishable independent if every party must have at least two members on the committee ,if in addition ,no group may have a majority of the committee.

In order to have majority , the number of member is one party must be greater than the number of member in other party.

This means that one of the party must have atleast 9 members.

a) Every party must have atleast two members on the committee

b) No group may have a majority of the committee members.

Since ,both parties cannot have 9 members thus on order to compute the committee number in a way that no group may have a majority of the committee members

orchestra answered 1 year ago

Next > < Previous

Related Solutions

How many ways are there to select a committee of 17 politicians chosen from a room...

How many ways are there to select a committee of 17 politicians chosen from a room full of indistinguishable Democrats, indistinguishable Republicans, indistinguishable Independents if every party must have at least two members on the committee? If, in addition, no group have a majority of the committee members?

A student council consists of 15 students. (a) In how many ways can a committee of...

A student council consists of 15 students. (a) In how many ways can a committee of five be selected from the membership of the council? (b) Two council members have the same major and are not permitted to serve together on a committee. How many ways can a committee of five be selected from the membership of the council? (c) Two council members always insist on serving on committees together. If they can't serve together, they won't serve at all....

6) A student committee has 15 members, including 7 from grade 12. In how many ways...

6) A student committee has 15 members, including 7 from grade 12. In how many ways can a 4 member subcommittee be formed if a. There are no restrictions, b. The subcommittee must be only grade 12s, c. The subcommittee must have only 2 grade 12s., and d. The subcommittee can have no more than 2 grade 12s?

How is The Federal Open Market Committee chosen and what is their job?

A committee of 2 women and 6 men is to be chosen randomly from a group...

A committee of 2 women and 6 men is to be chosen randomly from a group of 18 women and 13 men. a) What is the probability that "Ann" (female) and her friend "Bob" (male) are on the committee together? b) What is the probability that ``Ann''(female) and her friend ``Bob''(male) are on the committee and their friends ``Carla''(female) and ``Dan''(male) are also on the committee? c) Given that ``Carla'' and ``Dan'' have been chosen to be on the committee,...

A committee of 4 is chosen at random from a group of 7 women 5 men....

A committee of 4 is chosen at random from a group of 7 women 5 men. Find the probability that the committee contains at least one man. without replacement

How many ways can a Snail Darter Society, who has 25 members, elect an executive committee...

How many ways can a Snail Darter Society, who has 25 members, elect an executive committee of 2 members, an entertainment committee of 3 members, and a welcoming committee of 2 members if members can serve on at most 2 committees?

a. How many ways are there to rearrange the letters of Massachusetts? b. How many ways...

a. How many ways are there to rearrange the letters of Massachusetts? b. How many ways are there to rearrange such that M can't be at the beginning and A can't be at the end? c. How many ways are there to have the two t's consecutively (next to each other)?

(a) How many different committees consisting of 3 males and 4 females can be chosen from...

(a) How many different committees consisting of 3 males and 4 females can be chosen from a group of 8 males and 7 females? (b) In how many ways can 5 essays be ranked in a contest? (c) A license plate has three letters from 26 letters of an alphabet and four digits from 0,1,2,3,4,5,6,7,8,9. How many plates can be made if: i) letters and numbers cannot be repeated? ii) repetitions are allowed?

CRITICAL THINKING EXERCISE. The operating room environment is complex in many ways. One of the complexities...

CRITICAL THINKING EXERCISE. The operating room environment is complex in many ways. One of the complexities involves the way drugs are ordered, dispensed, handed over to scrubbed personnel, and nanded over to the surgeon for administration. The following statements about the drug process describe tasks and events that routinely occur in the operating room. How does each situation affect or cause specific drug errors? Provide one or more errors that can be attributed to the situation described. Be specific. 1....

Subjects