family game: how many combinations are possible?

Hi guys

I'm almost getting crazy. We are playing a game in our family and i wanted to demonstrate my son for what probability is useful. Now i am trying to solve following problem since 4 hours:

I have 5 different dices (blue, red, yellow, black, white) in an urn. I take one by one randomly out and roll it (order matters, no putting back). The possible numbers on all dices go between 1 and 3. How many different combinations do exist?

My first estimate was 3×5! (5 draws without putting it back), then i switched to 5×3^5. I tested it with 2 dices going from 1-3 and 3 dices going from 1-2 in a decision tree but i am not able to generalize it.

Really appreciating your help!

Happy easter, chris


TS Contributor
Each dice has 3 possible outcomes, so there are \( 3^5 \) combination when you rolling 5 dice.

Since the order is also important, you have to account for the permutation \( 5! \) for each combination. Therefore the total number is \( 3^5 \times 5! \)