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  • A game show has 8 questions, each with 4 possible answers. How many different ways can a contestant answer all 8 questions, if they are allowed to guess on every question and can choose t

A game show has 8 questions, each with 4 possible answers. How many different ways can a contestant answer all 8 questions, if they are allowed to guess on every question and can choose the same answer more than once?

 

 

 

 

Option: 1

35536


Option: 2

45563


Option: 3

65536

 


Option: 4

55363


Answers (1)

best_answer

For each of the 8 questions, the contestant has 4 possible answers. Therefore, using the multiplication principle of counting, we can find the total number of ways a contestant can answer all 8 questions is given by,

\mathrm{Total \: number\: of \: ways\: Number \: of \: ways\: to \: answer\: the\: first \: question\: \times \: Number \: of\: ways \: to\: answer\: the \: second \: question \: \times . . \times\: Number \: of \: ways\: to \: answer the\: eight \: question}\mathrm{Total \: number\: of \: ways\: Number \: of \: ways\: to \: answer\: the\: first \: question\: \times \: Number \: of\: ways \: to\: answer\: the \: second \: question \: \times . . \times\: Number \: of \: ways\: to \: answer the\: eight \: question}
Since the contestant can guess every question and choose the same answer more than once, there are 4 possible ways to answer each of the 8 questions. Therefore, we get:

\mathrm{Total\: number \: of \: ways =4 \times 4 \times 4 \times \ldots \times 4(8times )}
Simplifying this expression, we get,

The total number of ways \mathrm{=4^8}

Using a calculator, we can evaluate \mathrm{=4^8} to get,

The number of ways =65536

Therefore, there are 65536 different ways a contestant can answer all 8 questions if they are allowed to guess on every question and can choose the same answer more than once.

Posted by

Pankaj Sanodiya

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