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  4. In an admission test, there are 15 multiple choice questions. Each question is followed by 4 alternatives to choose. Out of these there may be one or more than one correct answers. If a student attempts all the 15 questions and marks the answers randomly, then number of different ways he can answer the question paper is

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Q. In an admission test, there are $15$ multiple choice questions. Each question is followed by $4$ alternatives to choose. Out of these there may be one or more than one correct answers. If a student attempts all the $15$ questions and marks the answers randomly, then number of different ways he can answer the question paper is

TS EAMCET 2018

Solution:

These are 15 multiple type questions. Students attempts all 15 questions.
The number of way student can answer the questions is $=m^{n}$
$m =15 $
$n =15 $
$\Rightarrow \, (15)^{15}$