# Thread: Permutation and Combination...The Difference

1. ## Permutation and Combination...The Difference

Given a basic probability question, what key word(s) make clear that it is a permutation or combination problem? I do not have a specific question. Can someone provide me with a word problem for each case?

Knowing that order does not matter for combination versus a permutation where order does matter tells me nothing when reading the word problem.

2. ## Re: Permutation and Combination...The Difference

Hello, nycmath!

Given a basic probability question, what key word(s) make clear
that it is a permutation or combination problem?

Usually there are no "key words" to warn us.
You must call on your "life experience" to interpret the situation.

"Form a committee of 3 people from 12 members."
Does the order of their names make a difference?
No, $\displaystyle \{A,B,C\}$ is the same committee as $\displaystyle \{B,C,A\}.$
This is a Combination.

"Form 3-letter words from the letters $\displaystyle \{A,C,O,T\}.$
Does the order of the letters make a difference?
Yes, $\displaystyle ACT$ is not the same as $\displaystyle C\!AT.$
This is a Permutation.

An amusing observation . . .

A combination lock has a set of three numbers used for unlocking.
But the three numbers must applied in a specific order.
So shouldn't it be called a permutation lock?

3. ## Re: Permutation and Combination...The Difference

Originally Posted by Soroban
Hello, nycmath!

Usually there are no "key words" to warn us.
You must call on your "life experience" to interpret the situation.

"Form a committee of 3 people from 12 members."
Does the order of their names make a difference?
No, $\displaystyle \{A,B,C\}$ is the same committee as $\displaystyle \{B,C,A\}.$
This is a Combination.

"Form 3-letter words from the letters $\displaystyle \{A,C,O,T\}.$
Does the order of the letters make a difference?
Yes, $\displaystyle ACT$ is not the same as $\displaystyle C\!AT.$
This is a Permutation.

An amusing observation . . .

A combination lock has a set of three numbers used for unlocking.
But the three numbers must applied in a specific order.
So shouldn't it be called a permutation lock?
Disregard the new inbox message on probability since you already answered this post. Thanks....

4. ## Re: Permutation and Combination...The Difference

Yes, it should be called a permutation lock but only math people would truly understand and appreciate its definition.