How Can I Master Complex Counting Problems Involving Multiple Principles?

[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.

 

[jedishrfu]

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.

 

[jedishrfu]

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