Enumeration Example
Suppose ABC University has 3 different math courses, 4 different business courses, and 2 different sociology courses. Tell me the number of ways a student can choose one of EACH kind of course. Then tell me the number of ways a student can choose JUST one of the course.

Enumeration - Handshakes
Consider the problem of how to arrange a group of n people so each person can shake hands with every other person. How might you organize this process? How many times will each person shake hands with someone else? How many handshakes will occur? How must your method vary according to whether or not n is even or odd?

Combinations & Permutations
What is the difference between combinations and permutations? What are some practical applications of combinations? Permutations?

Permutation Example
Find the number of permutations of A,B,C,D,E,F taken three at a time (in other words find the number of "3-letter words" using only the given six letters WITHOUT repetition).

Solution Preview

Enumeration Example
Suppose ABC University has 3 different math courses, 4 different business courses, and 2 different sociology courses. Tell me the number of ways a student can choose one of EACH kind of course. Then tell me the number of ways a student can choose JUST one of the course.

Answer: Since we have 3 choices to choose math, 4 choices to choose business and 2 choice to choose sociology, the number of ways a student can choose one of EACH kind of course=3*4*2=24
Since we only choose one course, the number of ways a student can choose JUST one of the course=3+4+2=9

Enumeration - Handshakes
Consider the problem of how to arrange a group ...

Solution Summary

The solution gives detailed steps for solving questions on enumeration, combination and permutation.

If the number of permutations of n objects taken r at a time is six times the number of combinations of n objects taken r at a time, determine the value of r. Is there enough information to determine the value of n? Why or why not?

In the design of an electrical product, 7 different components are to be stacked in a cylindrical casing that holds 12 components,in a manner that minimizes the impact of shocks.
One end of the casing is designated as the top and the other end the bottom.
a) how many different designs are possible
b) If the seven compon

Decide if the situation involves permutations, combination's or neither.
The number of ways 17 people can line up in a row for concert tickets.
Does the situation involve permutations, combination's or neither?
(choose correct answer a, b or c)
a) Permutations. The order of 17 people in line matters.
b) Neit

Please provide the formulas and 2 solved examples using the formulas for each of these topics:
The Multiplication Principle
Permutations
Combinations
Probability Applications of Counting Principles.

For each of the following, express your results in two ways: 1st, using the nPr or nCr notation, whichever is appropriate; 2nd, giving the numerical value:
a) The number of permutations of 8 objects taken 3 at a time
b) The number of combinations of 7 objects taken 5 at a time

1) How many different ways can a teacher select 2 books from a possible 17 books?
2) How many different ways can be made from a test bank of 20 questions if the test consists of 5 questions?
3) How many different ways can 4 tickets be selected from 50 tickets if each tickets wins a different prize?

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. In how many ways can we choose the committee?

A.Consider the partial order less than or equal to(<=) on the set X of positive integers given by "is a divsor of." Let a and b be two integers. Let c be the largest integer such that c<=a and c<=b and let d be the smallest integer such that a<=d and b<=d. What are c and d?
b. Prove that the intersection of R and S of two equ

An electronics store receives a shipment of 30 graphing calculators, including 3 that are
defective. Four calculators are selected to be sent to a local high school.
A. How many selections can be made using the original shipment?
B. How many of these selections will contain no defective calculators?