SOLUTION: A test has 6 multiple choice questions each having 4 possible answers. In how many ways can a student respond to the questions if: a) All questions must be answered? b) Not a

a)  All questions must be answered?    <<<---=== Answer.   ways.


       Solution


    For simplicity, let us assume that you write one of the 4 letters A, B, C or D as the possible answer to each question.

    Then you have 4 opportunities for each of 6 question, which gives the above answer.


    Memorize: the space of events in this case is the space of all 6-letter words written in 4-letter alphabet.




b)  Not all questions must be answered?       <<<---=== Answer.  .


       Solution


    We can very easily reduce this problem to the previous scheme by making an agreement that we write the fifth symbol/letter  "E"  

    where the question is unanswered.


    Then the space of events is the space of all 6-letter words written in 5-letter alphabet, which gives the above answer.