Problem 1174

If there are where multiple-choice questions on an exam, each having four possible answers, how many different sequences of answers are there?

 

Solution:-

 

If any one of k different mutually exclusive and collectively exhaustive events can occur on each of n trials, the number of possible outcomes is equal to kn.

The four possible answers to each multiple-choice question are mutually exclusive and collectively exhaustive. There are twelve questions.

K = 4 and n = 12

Substitute 4 for k and 12 for n in the expression kn and simplify.

kn = 412

=16777216

There are 16777216 different square of answers.

 

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