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Thread: family game: how many combinations are possible?

  1. #1
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    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 35! (5 draws without putting it back), then i switched to 53^5. 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

  2. #2
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    Re: family game: how many combinations are possible?

    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!

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    molly (04-15-2015)

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