/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 69 The ski club at Tasmania State U... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 16: Problem 69

The ski club at Tasmania State University has 35 members (15 females and 20 males). A committee of three members - a President, a Vice President, and a Treasurer must be chosen. (a) How many different three-member committees can be chosen? (b) How many different three-member committees can be chosen in which the committee members are all females? (c) How many different three-member committees can be chosen in which the committee members are all the same gender? (d) How many different three-member committees can be chosen in which the committee members are not all the same gender?

Short Answer

Expert verified
(a) 6545, (b) 455, (c) 1595, (d) 4950

Step by step solution

01

Total Different Committees

From a total of 35 members, any 3 members are selected. Using the combination formula, we calculate \(C(35, 3) = 35! / 3!(35 - 3)! = 6545.\)
02

All Female Committees

A committee consists of 3 female members only. From a total of 15 females, 3 females are selected. Therefore, using the combination formula, we calculate \(C(15, 3) = 15! / 3!(15 - 3)! = 455 .\)
03

All Same Gender Committees

A committee comprises 3 members of the same gender. This is a sum of two distinct cases - all females or all males. From Step 2, we know that the number of all female committees is 455. Now, calculate the number of all male committees by using the combination formula, \(C(20, 3) = 20! / 3!(20 - 3)! = 1140.\) Add these two values to get the total number of all same gender committees, 455 (females) + 1140 (males) = 1595.
04

Not All Same Gender Committees

A committee comprises 3 members of different or not all same genders. To calculate this, subtract the total number of same gender committees (1595, found in step 3) from the total number of committees (6545, found in step 1), 6545 - 1595 = 4950.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Using set notation, write out the sample space for each of the following random experiments. (a) A coin is tossed four times in a row. The observation is how the coin lands ( \(H\) or \(T\) ) on each toss. (b) A student randomly guesses the answers to a fourquestion true-or-false quiz. The observation is the student's answer ( \(T\) or \(F\) ) for each question. (c) A coin is tossed four times in a row. The observation is the percentage of tosses that are heads. (d) A student randomly guesses the answers to a fourquestion true-or-false quiz. The observation is the percentage of correct answers in the test.

Using set notation, write out the sample space for each of the following random experiments: (a) Three runners \((A, B,\) and \(C\) ) are running in a race (assume that there are no ties). The observation is the order in which the three runners cross the finish line. (b) Four runners \((A, B, C,\) and \(D)\) are running in a qualifying race (assume that there are no ties). The top two finishers qualify for the finals. The observation is the pair of runners that qualify for the finals.

Using set notation, write out the sample space for each of the following random experiments. (a) A coin is tossed three times in a row. The observation is how the coin lands ( \(H\) or \(T\) ) on each toss. (b) A basketball player shoots three consecutive free throws. The observation is the result of each free throw \((s\) for success, \(f\) for failure). (c) A coin is tossed three times in a row. The observation is the number of times the coin comes up tails. (d) A basketball player shoots three consecutive free throws. The observation is the number of successes.

The sample spaces are too big to write down in full. In these exercises, you should describe the sample space either by describing a generic outcome or by listing some outcomes and then using the ... notation. In the latter case, you should write down enough outcomes to make the description reasonably clear. A student randomly guesses the answers to a multiplechoice quiz consisting of 10 questions. The observation is the student's answer \((A, B, C, D,\) or \(E)\) for each question. Describe the sample space.

A pair of honest dice is rolled. Find the probability of each of the following events. (Hint: Do Exercise 13 first.) (a) \(E_{1}\) : "pairs are rolled." (A "pair" is a roll in which both dice come up the same number.) (b) \(E_{2}:\) "craps are rolled." ("Craps" is a roll in which the sum of the two numbers rolled is \(2,3,\) or \(12 .)\) (c) \(E_{3}:\) "a natural is rolled." (A "natural" is a roll in which the sum of the two numbers rolled is 7 or \(11 .\) )
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.