A survey consists of 10 questions. Each question has 5 possible answers. If each respondent is to be classified according to the number of responses of each type. How many categories are possible?
2007-01-13 11:25:55 · 3 answers · asked by brennen 1 in Science & Mathematics ➔ Mathematics
There are 9,765,625 categories.
If each quesion has 5 possible answers, then 5x5x5x5x5x5x5x5x5x5, or 5^10=9,765,625
That means that there are 9,765,625 ways that a person could answer the survey.
I hope that this helps.
2007-01-13 11:33:31 · answer #1 · answered by Anonymous · 1⤊ 0⤋
If I understand you correctly this problem could be phrased as how many ways can n questions be answered with r possible answers. The answer to that question is given by:
n(n-1)(n-2)(n-3).....(n-r+1)
so for your problem n= 10 and r = 5
therefore 10x9x8x7x6 = 30240
This problem is an example of the number of permutations of n different objects taken r at a time and is denoted by nPr. When n=r , nPn = n! i.e. n(n-1).....1
2007-01-13 19:54:33 · answer #2 · answered by 1ofSelby's 6 · 0⤊ 0⤋
50
2007-01-13 19:31:19 · answer #3 · answered by italianwiseass13 2 · 0⤊ 0⤋