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?

How many elements of order 5 are there in S_8?
- I think there are 8! / 3!5! = 56 ways to order the elements in the cycle but how many of order 5 are there?
keywords: S8

1. Find the effective rate of 8.5% compounded semianually.
2. Tony invested some money at 10% compounded quarterly at the end of three years his investment had grown to $2488.05. Find the initial investment.
3. Find the amount of an annuity with $2500 deposited quarterly at 8% for four years.
4. A sinking fund is e

I am studying perms and combs on my own for a course which i want to take in the future. I have come across 2 questions, to which I need a solution. I would also need the reasoning applied to the solution for future application. Here are the 2 questions.
Question 1. How many ways can 18 different vehicles be arranged in a c

Find the number of different selections of three letters which can be made from the letters of the word PARALLELOGRAM.
How many of these contain the letter P?

Please help with the following combinatorics problems.
Sarah, Jolly and Betty are female triplets. They and their 10 cousins are posing for a series of photographs. One pose involves all 13 children. How many ways can the 7 boys and 6 girls be arranged in one row under each of the following conditions?
a) The boys and gir

A person has 3 different letters to write, 2 interviews to do, and 2 commercials to review. In making aschedule, (first, second, etc.) how many different combinations are there?

Given the group {Allen, Brenda, Chad, Dorothy, Eric} you will be asked to determine
a. the number of ways of choosing a president, vice-president and secretary/treasurer. (3 points)
b. the number of ways of choosing a leadership team composed of 2 members. (3 points)
c. the number of ways of choosing a president, vice-

Modern Algebra
Group Theory (XIV)
Symmetric Set of Permutations
Symmetric Set of Permutations : Find order of all elements in S_3, where S_3 is the symme