1. In how many ways can ten items be selected from among fifteen items (a) if order is important? (b) if order is not important? 2. A club has 14 members. It plans to elect four officers – a president, a vice president, a secretary and a treasurer – by secret ballot. All 14 members are eligible and willing to serve. How many possible sets of four members can serve if you ignore the office held? How many sets can be formed if the office held is considered and each member can only hold one office? 3. In the Computer Company’s computer operations center, there are eight operators who must sit at one of eight individual machines that are placed one behind the other in a straight row. How many different ways could the eight operators be assigned to the eight machines? 4. The CEO of a company that produces seven different types of soup has a can of each type displayed in a row, on a credenza, in her office. (a) In how many different ways can she display the seven cans? (b) Suppose she wants to display only five of the cans at one time on the credenza. How many distinguishable arrangements are possible? 5.Two work teams, with six people on each team, are to be selected from a group of seventeen workers, with no one person serving on both teams at the same time. In how many ways can these teams be chosen? 6. Betty, Mark, and Jane belong to a club of eighteen people. A committee of twelve is to be selected at random from the membership. How many different arrangements of committee members are possible, given these facts? How many of these possible committees will definitely contain Betty, Mark, and Jane at the same time? 7.In how many ways can six people be selected from among thirteen people (a) if order counts? (b) if order does not count?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
1. In how many ways can ten items be selected from among fifteen items (a) if order is important? (b) if order is not important?
2. A club has 14 members. It plans to elect four officers – a president, a vice president, a secretary and a treasurer – by secret ballot. All 14 members are eligible and willing to serve. How many possible sets of four members can serve if you ignore the office held? How many sets can be formed if the office held is considered and each member can only hold one office?
3. In the Computer Company’s computer operations center, there are eight operators who must sit at one of eight individual machines that are placed one behind the other in a straight row. How many different ways could the eight operators be assigned to the eight machines?
4. The CEO of a company that produces seven different types of soup has a can of each type displayed in a row, on a credenza, in her office. (a) In how many different ways can she display the seven cans? (b) Suppose she wants to display only five of the cans at one time on the credenza. How many distinguishable arrangements are possible?
5.Two work teams, with six people on each team, are to be selected from a group of seventeen workers, with no one person serving on both teams at the same time. In how many ways can these teams be chosen?
6. Betty, Mark, and Jane belong to a club of eighteen people. A committee of twelve is to be selected at random from the membership. How many different arrangements of committee members are possible, given these facts? How many of these possible committees will definitely contain Betty, Mark, and Jane at the same time?
7.In how many ways can six people be selected from among thirteen people (a) if order counts? (b) if order does not count?
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
