Answer the questions below.(If necessary, consult a list of formulas.)(a) From a collection of 51 store customers, 3 are to be chosen to receive a special gift. How many groups of 3 customers are possible?(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.
Question
Answer the questions below.(If necessary, consult a list of formulas.)(a) From a collection of 51 store customers, 3 are to be chosen to receive a special gift. How many groups of 3 customers are possible?(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.
Solution
(a) The number of ways to choose 3 customers from a group of 51 is given by the combination formula C(n, r) = n! / [(n-r)! * r!], where n is the total number of items, r is the number of items to choose, and "!" denotes factorial.
In this case, n = 51 and r = 3.
So, C(51, 3) = 51! / [(51-3)! * 3!] = 51! / (48! * 3!)
This simplifies to (51 * 50 * 49) / (3 * 2 * 1) = 20825.
So, there are 20825 possible groups of 3 customers.
(b) The number of ways to fill 4 offices from a committee of 17 people is given by the permutation formula P(n, r) = n! / (n-r)!, where n is the total number of items, r is the number of items to choose, and "!" denotes factorial.
In this case, n = 17 and r = 4.
So, P(17, 4) = 17! / (17-4)! = 17! / 13!
This simplifies to (17 * 16 * 15 * 14) = 57840.
So, there are 57840 ways to fill the 4 offices.
Similar Questions
(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
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) A pizza parlor has a choice of 12 toppings for its pizzas. From these 12 toppings, how many different 7-topping pizzas are possible?(b) From a collection of 51 store customers, 3 are to be chosen to receive a special gift. How many groups of 3 customers are possible?
Answer the questions below.(If necessary, consult a list of formulas.)(a) A company that makes crayons is trying to decide which 5 colors to include in a promotional mini-box of 5 crayons. The company can choose the 5 mini-box colors from its collection of 75 colors. How many mini-boxes are possible?(b) How many different committees of size 3 can be formed from 14 people?
Answer the questions below.(If necessary, consult a list of formulas.)(a) 63 athletes are running a race. A gold medal is to be given to the winner, a silver medal is to be given to the second-place finisher, and a bronze medal is to be given to the third-place finisher. Assume that there are no ties. In how many possible ways can the 3 medals be distributed?(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 offices be filled? Assume that a committee member can hold at most one of these offices.
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.