Question

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 8 questions on the survey

Answer 1

40320 different surveys would be necessary ...

Explanation:

let's start small :

how many are required for 2 questions ?

well, 2 (we can either ask question 1 first and then question 2, or question 2 first and then question 1).

how many for 3 questions ?

well, we have a choice of 3 questions to be asked first. but then for the second and third question we are back in the previous problem of 2 (remaining) questions.

so, we multiply the 3 initial options with the 2 following options. 3×2 = 6

how many for 4 questions ?

well, we have a choice of 4 questions as first question, and then fit the rest we are back in the previous problem of 3 questions. 4×3×2 = 24

you see the pattern ?

yes, that continues as far as we want to go.

for our example the problem was about 8 questions.

so,

8×7×6×5×4×3×2 = 8! = 40320