Thread: Permutations and Combinations

I looked through Google and Im still confused about permutations and Combinations.

First off I understand that you use permutations when the order matters and combination if the order doesn't matter but I'm confused when to recognize a problem without the statement-the order matters-. Please help me! By giving me examples of the differences between the two.

When you have to make a collection of objects...that is when you have to pick up things...you use combination.

When you have to arrange a collection of objects...you use permutations. permutation is within a combination...i.e. on a collection of collection of objects.

Example:
You have 26 alphabets in english. No. of ways to pick 10 alphabets out of 26=C(26,10)...this will be the total no. of different collections of 10 objects out of 26.

For each of these collection, we can arrange the 10 alphabets to form words in 10! ways.

Originally Posted by Nimmy

Im still confused about permutations and Combinations.
First off I understand that you use permutations when the order matters and combination if the order doesn't matter but I'm confused when to recognize a problem without the statement-the order matters-. Please help me! By giving me examples of the differences between the two.

Suppose we have a club of twenty people.
How many ways can we select a president, vice president, secretary, and treasurer?
That is a permutation.

How many ways can we select a committee of four to plan the end of school party?
That is a combination.

Subsets are counted using combinations.
Finite sequences are counted with permutations.

Originally Posted by Plato

Suppose we have a club of twenty people.
How many ways can we select a president, vice president, secretary, and treasurer?
That is a permutation.

How many ways can we select a committee of four to plan the end of school party?
That is a combination.

Subsets are counted using combinations.
Finite sequences are counted with permutations.

Let me get this straight...so this is a permutation because you can ONLY have one president, one vice president, One Secretary and One Treasurer?

Combination because unlike the first example, we can rearrange the ways any order we want?

Permutations are order driven. Yes having A as president and B as vice president is completely different from having B as president and A as vice president.

On the other hand, combinations are content driven.
A & B can be committee members without regard to order.

Plato,

I have a question why is a stack of 18 tests permutation and two flavors of ice cream combination?

I thought the order doesnt matter with the stack of 18 tests.

Here you would have been required to arrange the tests in the stack..I suppose


Two flavours of ice-cream is a combination only when you have more than two flavours at your disposal. If there are only two flavours, then there is only one combination. But if there are more than, you have choice to make a combination of 2.