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

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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