Permutation on dice

[spool25]

I am helping my daughter with homework. We have the following problem


In your turn at a certain game, you roll five different-colored dice.

how many out comes are possible?

We know the answer is 7776 but using the nPr formula how do you get that answer. We have tried various ways and have not even come close. I know 6^5 would work and so would 6*6*6*6*6 but these are not allowed to be used. Any help would be very appreciated.

 

[tkhunny]

Why are there prohibitions?

There are five dice and you are rolling them. You have said nothing of the numbers on the dice. There is, then, only one outcome. All five dice will land somewhere.

Seriously, what a silly problem.

 

[spool25]

Why are there prohibitions?

There are five dice and you are rolling them. You have said nothing of the numbers on the dice. There is, then, only one outcome. All five dice will land somewhere.

Seriously, what a silly problem.

I had the same questions when I saw the problem she was sent home with. That is the reason I am stuck. What I would consider a logical conclusion she has prohibited in her rules for the question. Also with no mention of numbers on the dice it also leaves you to guess at how many numbers.

 

[soroban]

Hello, spool25!

In your turn at a certain game, you roll five different-colored dice.
How many outcomes are possible?

We know the answer is 7776, but using the nPr formula, how do you get that answer?
We have tried various ways and have not even come close.
I know 6^5 would work and so would 6*6*6*6*6,
but these are not allowed to be used. . Really? .Who said so?

Your reasoning is correct.

With 5 distinguishable dice, there is no way to use the Permutation Formula.


If that restriction was made by her teacher, give her this problem:

You have three different colored shirts and four different colored slacks.
How many outfits (one shirt and one slack) can you form?

Challenge her to use the Permutation Formula to come up with the answer: 12