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.

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, $\displaystyle \{A,B,C\}$ 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*?

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, $\displaystyle \{A,B,C\}$ 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....

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.