Purchase Solution

Democrats and Republicans on Task Force

Not what you're looking for?

Ask Custom Question

A certain city has experienced a relatively rapid increase in traffic congestion in recent times. The mayor has decided that it's time to do something about the problem and decides to form a task force to research the causes of the problem and come up with suggestions for dealing with it. The mayor first compiles a list of names of 21 residents who will be considered for membership on the task force. Twelve of those 21 people are Republicans, and the other 9 are Democrats. How many ways are there to form a task force of 7 people from that list of 21 candidates if at least one member of the task force has to be a Republican and at least one member has to be a Democrat?

Purchase this Solution
Solution Summary

First, the general problem of forming a task force of 7 people from a group of 21 people is addressed. Then the requirement that there be at least one Democrat and at least one Republican on the take force is dealt with.

Solution Preview

The total number of ways to form a task force of 7 members from a group of 21 people is C(21, 7), the number of combinations of 7 "objects" taken from a set of 21 "objects" (sometimes called "21 choose 7" or denoted by 21C7).
Recall that:

C(21, 7) = (21!)/[(7!)(21 - 7)!]

= (21!)/[(7!)(14!)]

Now 21! (21 factorial), which is the product of the first 21 positive integers,
can be written as (21)(20)(19)(18)(17)(16)(15)(14!). Thus

C(21, 7) = (21)(20)(19)(18)(17)(16)(15)(14!)/[(7!)(14!)]

Canceling the 14! in the numerator against the 14! in the denominator, we find that

C(21, 7) = (21)(20)(19)(18)(17)(16)(15)/(7!)

= (21)(20)(19)(18)(17)(16)(15)/[(7)(6)(5)(4)(3)(2)(1)]

Note that 21 = 7(3), so dividing the numerator and denominator
by 21 (= 7(3)), we have

C(21, 7) = ...

Solution provided by:
Georgia Martin, PhD
Education
  • AB, Hood College
  • PhD, The Catholic University of America
  • PhD, The University of Maryland at College Park
Recent Feedback
  • "Thanks for your assistance. "
  • "Thank you. I understand now."
  • "Super - Thank You"
  • "Very clear. I appreciate your help. Thank you."
  • "Great. thank you so much!"
Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Probability Quiz

Some questions on probability

View More Free Quizzes
Related BrainMass Solutions

  • A simple algebra word problem

    There are x+10 Democrats (10 more than republicans). Number of republicans + number of democrats = number of senators In terms of x, x+(x+10)=100 2x+10=100 2x=100-10 2x=90 x=90/2=45 So there are 45 republicans and 45+10=55 democrats.

  • Hypothesis testing problems

    Voters Assume that a 2005 poll of 1000 American voters found that 76% of Republicans favored ending the tax on dividend income, as did 42% of Democrats and 54% of Independents.

  • Hypothesis testing for proportions

    Senate and Congress (House of Representatives) democrats who are in favor of a new modest tax on "junk food". Let p2 represent the population proportion of U.S.

  • Differed Approaches to Education from Democrats and Republicans

    https://www.brookings.edu/blog/brown-center-chalkboard/2015/08/03/how-far-apart-are-democrats-and-republicans-on-school-reform/ https://www.ascd.org/blogs/what-the-democrats-and-republicans-stand-for-on-education-excerpts-from-party-platforms In

  • Statistical test to examine differences in attitudes

    Thus, in our study the null hypothesis would be there is no difference between the means of Democrats, Republicans, and Independents on the Attitudes Toward Health Care Reform Scale.

  • Z test for equality of proportions.

    Answer The null hypothesis tested is H0: There is no significant difference in the proportion of Republicans and Democrats who favor the lowering of environmental standards The alternative is H1: The proportion of Democrats who favor the lowering

  • Permutations and Combinations of Committees

    32325 Permutations and Combinations of Committees We wish to form a committee of 7 people chosen from 5 democrats, 4 republicans, and 6 independents. The committee will contain 2 democrats, 2 republicans, and 3 independents.

  • Probability

    81870 To determine probability using probability tree The Senate consists off 100 senators, of whom 34 are Republicans and 66 are Democrats. A bill to increase defense appropriations is before the Senate.

  • Formation & Evolution of the 2 American Parties

    Interview conducted on August 7th 2014 www.ushistory.org An expert cites sources about the evolution of our two political parties from the Federalists and Democratic-Republican parties, to the Whigs and Democrats, to the modern day Democrats and Republicans

View More Related Solutions