(b) A certain committee consists of 17 people. From the committee, a president, a vice-president, a secretary, and a treasurer are to be chosen. In how many ways can these 4 offices be filled? Assume that a committee member can hold at most one of these offices.,840
Question
(b) A certain committee consists of 17 people. From the committee, a president, a vice-president, a secretary, and a treasurer are to be chosen. In how many ways can these 4 offices be filled? Assume that a committee member can hold at most one of these offices.,840
Solution
The problem involves the concept of permutations, which is a way of arranging items where the order is important.
Step 1: Identify the total number of items. In this case, we have 17 people.
Step 2: Identify the number of positions to be filled. Here, we have 4 positions (president, vice-president, secretary, and treasurer).
Step 3: Use the formula for permutations, which is nPr = n! / (n - r)!, where n is the total number of items, r is the number of items to choose, and "!" denotes factorial.
Step 4: Substitute the values into the formula. So, we have 17P4 = 17! / (17 - 4)!
Step 5: Simplify the equation. 17! / 13! = 17 * 16 * 15 * 14 = 57840.
So, there are 57,840 ways these 4 offices can be filled from a committee of 17 people.
Similar Questions
Answer the questions below.(If necessary, consult a list of formulas.)(a) A certain committee consists of 18 people. From the committee, a president, a vice-president, and a treasurer are to be chosen. In how many ways can these 3 offices be filled? Assume that a committee member can hold at most one of these offices.(b) From a collection of 52 store customers, 2 are to be chosen to receive a special gift. How many groups of 2 customers are possible?
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? (Type an integer or a simplified fraction.)
A committee of five is to be selected from a class of 30 students.(a) In how many ways can this be done?(b) After the committee is selected, one person is elected chairperson and another is elected secretary. In howmany ways can these positions be filled?
Answer the questions below.(If necessary, consult a list of formulas.)(a) There are 16 appetizers available at a restaurant. From these, Abdul is to choose 12 for his party. How many groups of 12 appetizers are possible?(b) A certain committee consists of 16 people. From the committee, a president, a vice-president, and a treasurer are to be chosen. In how many ways can these 3 office
A committee of six is chosen from 14 people. In how many ways can this be done?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.