How Can I Master Complex Counting Problems Involving Multiple Principles?

Ex: Counting Problem Using CombinationsEx: Counting Problem Using Combinations - Repeated ItemsEx: Counting Problem Using Combinations - Repeated ItemsEx: Counting Problem Using Combinations - Repeated Items
  • #1
member 587159

Homework Statement



Counting problems are a very tough subject to me, so if someone could give me tips, examples explaining what's really happening, that would be great.

Homework Equations



I know what permutations, variations, combinations, ... are. The problems involving only one of those are do-able, but those that combine more than one are the difficult ones for me.

The Attempt at a Solution



I do not really have a certain problem as I find most exercises rather difficult.[/B]

Thanks in advance.
 
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  • #2
You could check out Khan Academy and watch videos on the subject;

https://www.khanacademy.org/math/precalculus/prob-comb/combinations/v/introduction-to-combinations

Start with a simple problem:

How many 3 letter words can I make?

How many 3 letter words can I make with the first letter is a consonant?

How many 3 letter words can I make with the first letter a consonant and the second letter a vowel?

then do the same problems with the restriction that no letter can be repeated.

Think up your own problems and post them here with your work for us to comment on.
 
  • #3
Here's some more videos from MathIsPower4U.com under Algebra 2:

https://dl.dropboxusercontent.com/u/28928849/Webpages/Algebra2VideoLibraryTable.htm

under column 3 you'll find this list of videos:

Counting and Probability
Counting Principle

The Counting Principle
Ex: Determine the Number of Possible Outfits - Counting Principle
Ex: Determine the Number of Three Letter Codes - Counting Principle
Ex: Determine the Outcomes Rolling Colored Dice - Counting Principle
Ex: Determine the Number of Possible License Plates - Counting Principle
Ex: Determine the Number of Ways to Complete a True/False Test - Counting Principle

Permutations and Combinations

Permutations
Ex: Evaluate a Combination and a Permutation - (n,r)
Ex: Evaluate a Combination and a Permutation - (n,1)
Ex: Determine the Number of Ways Six Runners Can Finish - Counting/Permutation
Ex: Determine the Possible Number of 4 Color Striped Flags (Permutation)
Ex: Determine the Possible Number of of Ways 255 Contestants can Win 3 Prizes (Permutation)
Ex1: Determine the Number of Permutations With Repeated Items
Ex2: Determine the Number of Permutations With Repeated Items
Combinations
Ex: Determine the Number of Ways 6 Books can be Selected from 9 Books (Combination)
Ex: Determine the Number of Ways 3 Varieties can be Selected from 12 (Combination)
Ex: Determine the Number of 4 Topping Pizzas from 14 Toppings (Combination)
Ex: Determine the Number of 4 Card Hands from 52 Cards
Solving Counting Problems
 
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1. How do you approach counting problems?

When approaching counting problems, it is important to first identify the type of problem and the given parameters. Then, determine if the problem requires a permutation or combination formula, and apply the appropriate formula to solve the problem.

2. What is the difference between permutations and combinations?

Permutations are arrangements where the order matters, while combinations are selections where the order does not matter. Permutations are used when order is important, such as arranging a sequence of events, while combinations are used when order does not matter, such as selecting a group of people.

3. How do you determine if a problem requires a permutation or combination formula?

The wording of the problem can give clues as to whether a permutation or combination formula should be used. If the problem involves arranging or ordering items, a permutation formula should be used. If the problem involves selecting a group of items, a combination formula should be used.

4. Can you provide an example of a counting problem?

Sure! An example of a counting problem would be: In how many ways can a committee of 4 people be chosen from a group of 10 individuals? This problem requires a combination formula, as the order of the committee members does not matter.

5. How can I check my work for counting problems?

To check your work for counting problems, you can use the fundamental counting principle. This states that if a problem can be broken down into smaller, simpler steps, the total number of possibilities is the product of the number of choices at each step. You can also use a calculator or software program to verify your answer.

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