Combinations and Probability

A series of college algebra lectures: Solving Problems Involving Permutations, Solving Problems Involving Combinations, Independent Events, Inclusive Events

Solving Problems Involving Permutations
Examples:

1. A museum has 7 paintings by Picasso and wants to arrange 3 of them on the same wall. How many ways are there to do this?
   
2. How many ways can you arrange the letters in the word LOLLIPOP?
   
3. A person playing poker is dealt 5 cards. How many different hands could the player have been dealt?

Permutation & Combination Application/Word Problems
Example:

1. In how many ways can a president and a vice president be selected from a committee of 32 people.
   
2. An organization with 23 members is to select 7 chairman, with each member having equal authority. In how many ways can this be done?
   
3. A club consists of 12 men and 15 women. In how many ways can this club choose a president, vice-president, treasurer, and secretary along with an advisory committee of 5 people?
   
4. A state allows personalized license plates with 6 spaces. These spaces can be filled either with numbers 0 - 19, letters A - Z, or any of the following symbols: β, η, −, δ, ϕ. What is the total number of personalized license plates that could possibly be made using this counting scheme?
   
5. A student answers 8 out of 10 questions on an exam. How many different ways can the selected 8 questions be answered?
   
6. A typical social security number looks as follows: 777-93-1111. How many social security numbers can be made up if you restrict the first 2 digits from being zero and the last 2 digits from being zero or nine?

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Independent Events

Inclusive Events

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