probability
posted by mathfailure .
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 
PsyDAG
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 
mathfailure
so is it 1/27?

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

probability 
Damon
Each game is independent so yes.
Respond to this Question
Similar Questions

Math
If I have 4 people and I want to take a picture of them standing side by side, how many total different combinations can I use? 
math but also probability
Three people play a game of "nonconformity": They each choose rock, paper, or scissors. If two of the three people choose the same symbol, and the third person chooses a different symbol, then the one who chose the different symbol … 
Statistics
Over time, a student analyzes her ability to guess correctly after narrowing down multiple choice answers in a 5selection question (a through e). She discovers that if she narrows her answers to 2 or 3 choices, her probability of … 
PROBABILITY QUESTION PLEASE HELP!!
Three people play a game of "nonconformity": They each choose rock, paper, or scissors. If two of the three people choose the same symbol, and the third person chooses a different symbol, then the one who chose the different symbol … 
Probability Word Problem
Julie has three choices of a lunch and 4 choices of a drink. How many different ways can she choose a lunch and a drink? 
Math (Probability)
Four players are playing a game involving choosing squares on a grid of size 3×8. Each player chooses a random square on the grid, then all players reveal their choices and a token is placed in the center of each of these squares. … 
Math (Probability)
Four players are playing a game involving choosing positions on a grid of size 3×8. Each player chooses a random position on the grid, then all players reveal their choices and a token is placed on each of the positions. The probability … 
MATH PLEASE HELP THIS IS A TEST!!!!!!!!!!!!!!!!
Which events are NOT independent? Landing on heads after tossing a coin and rolling a 3 on a 6 sided number cube Choosing a marble from a jar and landing on tails after tossing a coin Choosing a 5 from a deck of cards replacing it 
Math Probability
Mario, Yoshi, and Toadette play a game of "nonconformity": They each choose rock, paper, or scissors. If two of the three people choose the same symbol, and the third person chooses a different symbol, then the one who chose the different … 
EPI
Is creating a responsible budget, savings and investing, and establishing credit worthiness show any key economic principles?