-2
$\begingroup$

I'm working on this problem.

6 dice are tossed, what's the probability that all dice 1,2,3,4,5,6 in that order.

  • 3
    How do we get numbers in order if the dice are tossed simultaneously?2017-02-14
  • 1
    Assuming they all land simultaneously as well, the probability of landing in order is zero .... Maybe it's a trick question?!2017-02-14
  • 1
    total possible choices are 6^62017-02-14
  • 0
    Maybe they are coloured dice and we take results in ROYGBV placement, or they are rolled against a stopper board, such as on a crap table, or some such order imposing structure.2017-02-14
  • 0
    I assumed they were tossed at the same time, but it isnt, it's one by one2017-02-14

1 Answers 1

2

The probability of rolling $123456$ with six dice in a single roll can be expressed as: $$P(\text {second die does not match first die})\times P(\text {third die does not match first or second die}) \times \cdots$$ $$ = 1\times \frac {5}{6} \times \frac {4}{6} \times \frac {3}{6} \times \frac {2}{6} \times \frac {1}{6} = 0.015432$$

Hope it helps.

  • 0
    what about if the dice are tossed one by one?2017-02-14
  • 2
    @ColonelG If tossed one by one, then the outcome of one die is not affected by the outcome of the others, so we have a probability of $(\frac{1}{6})^6$.2017-02-14