Permutation and Combination...The Difference

• Jun 7th 2014, 06:37 AM
nycmath
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.
• Jun 7th 2014, 08:33 AM
Soroban
Re: Permutation and Combination...The Difference
Hello, nycmath!

Quote:

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, $\{A,B,C\}$ is the same committee as $\{B,C,A\}.$
This is a Combination.

"Form 3-letter words from the letters $\{A,C,O,T\}.$
Does the order of the letters make a difference?
Yes, $ACT$ is not the same as $C\!AT.$
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?
• Jun 7th 2014, 09:31 AM
nycmath
Re: Permutation and Combination...The Difference
Quote:

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, $\{A,B,C\}$ is the same committee as $\{B,C,A\}.$
This is a Combination.

"Form 3-letter words from the letters $\{A,C,O,T\}.$
Does the order of the letters make a difference?
Yes, $ACT$ is not the same as $C\!AT.$
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....
• Jun 7th 2014, 09:34 AM
nycmath
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.