Chapter 9.1, Problem 42E

Solution

To state: The number of answer keys which are possible for a 10-question multiple-choice test in which each question leads to choice $a,b,c,d,\text{or}e$ .

The resultant value is 9,765,625 answer keys.

Given information:

There is a 10-question multiple-choice test for which answer keys has to be made.

Explanation:

The answer of a question has 5 possible chances $a,b,c,d,\text{or}e$ .

For the first question 5 possibilities. Similarly for the second question, again there are 5 possibilities. Thus it can be said that for each question there are 5 possibilities.

If an answer key is to be made then for 10 questions, the required numbers of ways for setting an answer key are:

  $5\cdot 5\cdot 5\cdot 5\cdot 5\cdot 5\cdot 5\cdot 5\cdot 5\cdot 5=9765625$

Therefore, there are 9,765,625 ways in which these questions can be answered.