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Chapter 6: Problem 13

A computer dating service uses the results of its compatibility survey for arranging dates. The survey consists of 50 questions, each having five possible answers. How many different responses are possible if every question is answered?

Short Answer

Expert verified
There are \(8,881,376,961,245,063,916,907,891,074,632,081\) different responses possible if every question is answered on the computer dating service's compatibility survey.

Step by step solution

01

Identify the number of possibilities for each question

Each question in the compatibility survey has five possible answers.
02

Calculate the total number of possibilities for all questions

Since there are 50 questions, each with five possible answers, we can find the total number of different responses by multiplying the possibilities for each question together. We have: Responses = (Possibilities for Question 1) 脳 (Possibilities for Question 2) 脳 ... 脳 (Possibilities for Question 50) Since each question has five possible answers, this is equivalent to: Responses = \(5^{50}\)
03

Calculate the result

Using a calculator, compute the value of \(5^{50}\). The result is: Responses = 8,881,376,961,245,063,916,907,891,074,632,081 So, there are 8,881,376,961,245,063,916,907,891,074,632,081 different responses possible if every question is answered on the computer dating service's compatibility survey.

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