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 Question from Sueheir, a parent: I have a survey of 9 independent questions. Each of the 9 questions has the following answers (Good, average, poor) occurring equally likely. How many different combinations of answers do I have ? What is the probability of each combination? how many similar combinations do I have?... thanks a lot!

Sueheir,

If there was only one question then there would be 3 possible answers

G, A or P

Now add a second question. Anyone taking the survey could answer the second question G, A or P regardless of how they answered the first question. Thus for a two question server there are 3 3 = 32 = 9 possible answers

GG, GA, GP,
AG, AA, AP,
PG, PA, PP

Now add a third question. Any of the possible two question responses above can be extended to a three question response by appending a G, A or P. Thus there are 33 = 27 possible combination to a three question survey.

You should be able to complete it now.
Penny

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