Consider a political discussion group consisting of 15 Democrats, 11 Republicans, and 8 Independents. 1. Find the number of three person subcommittees that can be made by choosing any republican, any democrat, and any independent. 2. Find the total number of possible 5 person subcommittees that can be chosen if the members can be any of the 34 people in the group. 3. Find the number of ways the Republicans can choose a subcommittee of 4 members. 4. Find the number of ways the Democrats can choose a subcommittee of 3 members. 5. Find the number of ways the Independents can choose a subcommittee of 3 members. 6. Find the number of ways the Independents can choose a Chairperson, Vice-chairperson, and Secretary, in this order. 7. Find the number of ways the Republicans can choose a Chairperson, Vice-chairperson, and Secretary, in this order. 8. Find the number of ways the Democrats can choose a Chairperson, Vice-chairperson, and Secretary, in this order.

Question

Today at 2:42 AM
Mathematics

Answered

Consider a political discussion group consisting of 15 Democrats, 11 Republicans, and 8 Independents. 1. Find the number of three person subcommittees that can be made by choosing any republican, any democrat, and any independent. 2. Find the total number of possible 5 person subcommittees that can be chosen if the members can be any of the 34 people in the group. 3. Find the number of ways the Republicans can choose a subcommittee of 4 members. 4. Find the number of ways the Democrats can choose a subcommittee of 3 members. 5. Find the number of ways the Independents can choose a subcommittee of 3 members. 6. Find the number of ways the Independents can choose a Chairperson, Vice-chairperson, and Secretary, in this order. 7. Find the number of ways the Republicans can choose a Chairperson, Vice-chairperson, and Secretary, in this order. 8. Find the number of ways the Democrats can choose a Chairperson, Vice-chairperson, and Secretary, in this order.

Answer :

Other Questions

For a monopolist to sell an output level of 10 units, the price must be $8. MR at this output level will be Multiple Choice > $8 and < $16. < $8. > $16. = $8.

Sonkoly 2008. MicroRNAs and immunity: novel players in the regulation of normal immune function and inflammation

When defining a class, the class should be composed of the kind of values a variable of the class can contain, and

Which two features present the strongest evidence for establishing evolutionary relationships between species

It takes $1200$ workers $8$ years to build $3$ ziggurats. How many years would it take $100$ workers to build $1$ ziggurat

20 miles in km. please help

Y = sinx.logx.x^4. find dy/ dx.

20. When did you send the message?EXERCISE 2: Change the Verbs in the following sentences from Passive Voice to Active Voice. Alsmake other necessary changes.1.

1. Cultivation on planter's own land was calleda) Nijb) Ryotc) Ryoti

differentiate between minicomputers, microcomputers and mainframe. 2 to 3 lines answer

After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 55.0 cmcm. She finds that the pendulum makes 110 complete swings

Which is not a preposition? 1. after 2. near 3. under 4. who

Which of the following has a primary role in attacking cancer cells and protecting against some pathogens by killing harmful cells on contact

If the concentration of the acid is represented by the variable x, then what should you use to represent the concentration of the base so you can solve for the

A sample of aluminum metal is placed in a graduated cylinder. It is noted that 5.50 mL of water is displaced by the aluminum. The aluminum is then reacted with

What is the most likely reason Odysseus begins his story by telling his audience how well known he is for his great deeds, and who his father is

The three steps for constructing a simple frequency distribution are Group of answer choices find the observed range, find the interval width, and construct the

quizlet Governments implement Blank trade policies that are designed to make it difficult for imports to enter a country.Multiple choice question.residualvalore

At a certain fast food restaurant, 77.5% of the customers order items from the value menu. If 14 customers are randomly selected, what is the probability that a

Julian buys plants and flowers every month. Both are normal goods. When the price of flowers fell, Julian purchased fewer plants. Which of the following stateme

Ike125 Ike125 · Answer 1 · 2025-04-14T02:47:47-04:00

Answer:

1) 1320 2)278256 3)330 4) 455 5)56 6)336 7) 990 8) 2730

Step-by-step explanation:

Solution:

1) Democrats = 15, Republicans = 11, Independents= 8

Total = 15+ 11+ 8 =34

Number of 3 persons committee = 15nCr 1 * 11nCr1 * 8nCr1

nCr =combination

Number of 3 persons committee that can be made by choosing any republican or democrat or independent = 15 * 11* 8 =1320

2)Total number of possible 5 person subcommittes from any 34 people = 34nCr5 = 34!/(29! * 5!)

=278256

3) Number of ways republicans choose subcomittee of 4 members = 11nCr4

= 11!/(7! * 4!)=330 ways

4) Number of ways democrats choose subcomittee of 3 members = 15nCr3

= 15!/ (12! *3!)=455 ways

5) Number of waysindependents choose subcomittee of 3 members = 8nCr3

= 8!/(5! * 3!)= 56 ways

6) Number of ways independents choose chairperson, vice chairperson and secretary:

As one picks each post the number of person decreases

= (Chairperson)* (vice chairperson) * (secretary) = 8nCr1 * 7nCr1 * 6nCr1

=336 ways

7) Number of ways republicans can choose chairperson, vice chairperson and secretary

As one picks each post the number of person decreases

= (Chairperson)* (vice chairperson) * (secretary) = 11nCr1 * 10nCr1 * 9nCr1

= 990ways

8) Number of ways Democrats can choose chairperson, vice chairperson and secretary

As one picks each post the number of person decreases

= (Chairperson)* (vice chairperson) * (secretary) = 15nCr1 * 14nCr1 * 13nCr1

= 2730 ways