# probability

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Im not good at probability.

If there are 3 choices, and 3 people can choose any of them, what are the odds of the 3 people choosing all different choices?

• probability -

Each person has a 1/3 probability of making the choice from 3.

The probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

• probability -

so is it 1/27?

• probability -

There are 3! = 6 ways to assign the possible choices that are all different to the persons. The total number of choices, irrespective if they are all different or not, is 3^3 = 27.

The persons are randomly sampling from the set of 27 total choices, the probability that such a choice belongs to the subset of 6 that are all different is thus 6/27 = 2/9.

• probability -

what if this is a game, and we play like 4 rounds? Would it be 2/9 ^4?

• probability -

Each game is independent so yes.

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