A pollster wants to minimize the effect the order of the questions has on a person's response to a survey. How many different surveys are required to cover all possible arrangements if there are 5 questions on the survey?
To minimize the effect of the order of the questions on a person's response, the pollster needs to consider all possible arrangements of the questions.
The number of different surveys required to cover all possible arrangements can be determined using the concept of permutations.
In this case, we have 5 questions on the survey. The number of possible arrangements of these questions can be calculated as follows:
5! (5 factorial) = 5 x 4 x 3 x 2 x 1 = 120
Therefore, the pollster would need 120 different surveys to cover all possible arrangements of the 5 questions.
To calculate the number of different surveys required to cover all possible arrangements of 5 questions, we can use the concept of permutations.
The number of permutations of a set of objects is given by the factorial of the number of objects. In this case, we want to find the number of permutations of 5 questions.
The formula for permutations is: nPr = n! / (n - r)!
Where n is the total number of objects (5 questions) and r is the number of objects selected (also 5 questions).
Therefore, the formula becomes: 5P5 = 5! / (5 - 5)!
Simplifying, we get: 5P5 = 5! / 0!
The factorial of 5 is 5! = 5 x 4 x 3 x 2 x 1 = 120.
The factorial of 0 is defined as 1 by convention.
Therefore, the number of different surveys required to cover all possible arrangements of 5 questions is 120.
Number of choices for the first question=5
Number of remaining choices for the second question = 4
....
Number of remaining choices for the last question = 1
Number of possible arrangements = 5*4*...*1