## anonymous 5 years ago A mutiple choice test consists 8 questions with each question having 2 possible answers. how many different ways are there to mark the answers?

1. anonymous

2. anonymous

just one more!

3. anonymous

Use the product rule.

4. anonymous

and it would come up to?

5. anonymous

you tell me?

6. anonymous

7. anonymous

You have 8 question, and you can answer each question 2 ways, how many total ways can you answer?

8. anonymous

16

9. anonymous

Nope

10. anonymous

its 8 questions and u can answer it 2 different ways which it doubles

11. anonymous

If it were just 2 questions with 2 ways to answer, how may ways would there be to fill the test?

12. anonymous

2

13. anonymous

2^2

14. anonymous

Actually that's a bad example. If there were 3 questions with 2 ways to answer each how many ways

15. anonymous

I'm not asking you cantor ;p

16. anonymous

ok :)

17. anonymous

in the same way but just with 3

18. anonymous

Lets say it's a true false test with 3 questions. I can answer True, True, True False, True, True True, False, True False, False, True True, True, False False, True, False True, False, False False, False, False Right?

19. anonymous

Yeah I know that

20. anonymous

So how many is that?

21. anonymous

25

22. anonymous

Really? Cuase I only count 8 different ways I can do the test.

23. anonymous

Err Cause rather.

24. anonymous

theres 8 ways but all toghether theres 25 if u count the true false's

25. anonymous

No. There are 8 different possible ways to complete the test.

26. anonymous

25 ????????????????

27. anonymous

So for your original question if you have 8 questions, how many possible ways can you complete the test?

28. anonymous

29. anonymous

if u count them all toghether u get 25 thats how so stop u guys are suppose to help not be mean

30. anonymous

sorry i was talking to polpak

31. anonymous

w.e bye someone else will help me

32. anonymous

33. anonymous

well when it's done and outta the way I will not have to look back at it so..

34. anonymous

except when it's time to take the test, or when something new is taught that uses this to solve, etc.

35. anonymous

Everything builds on everything else

36. anonymous

ur helping everyone else and giving them answeers?

37. anonymous

pol, she added up all of them, she cant count either , there are 24 in that list

38. anonymous

Yeah

39. anonymous

there's 25

40. anonymous

no theres 24

41. anonymous

There are 8 lines, with 3 words on each line.

42. anonymous

This is one of those things you got someone to tell you and didn't look back about I can see.

43. anonymous

i didnt even think of that,

44. anonymous

$8\times 3 \ne 25$

45. anonymous

right

46. anonymous

pol, so your integration seems redundant

47. anonymous

hrm?

48. anonymous

its 2 not 3

49. anonymous

50. anonymous

well, 8*2 is certainly not 25.

51. anonymous

sure

52. anonymous

you mean 8 *3

53. anonymous

its 16

54. anonymous

she cant count and doesnt reason well.

55. anonymous

I do mean 8*3, but she claimed it was 2, not 3.

56. anonymous

the problem states 3 not 2

57. anonymous

wait, i guess theres some subtley here. let me see

58. anonymous

2 not 3

59. anonymous

Erg. Ok look chika. I enumerated the possible outcomes for a test with 3 questions where each question had 2 answers.

60. anonymous

ok each of those lines is ONE possibility for the test to be solved

61. anonymous

Each line in my post was a way you could complete the whole test. Not one question.

62. anonymous

so you wrote out the entire sample space

63. anonymous

Try something more simple. If you have two true or false questions how many ways can you answer them?

64. anonymous

I didn't want to try to write out the sample space for 8 questions because a) that would have given her the answer, and b) I didn't want to write 256 lines.

65. anonymous

the other way is to use multiplication rule for the first question there are 2 ways, second question there are 2 ways to answer, etc, so the total ways is 2 x 2 x 2 ...

66. anonymous

kind of like a tree diagram

67. anonymous

so you can enumerate the entire space, as you did pol for your simpler example. or you can use product rule rather than enumerate 256 cases

68. anonymous

o wait

69. anonymous

I got it

70. anonymous
71. anonymous

chika, how did you get 25 !!!

72. anonymous

73. anonymous

pol, it is redundant because you already have cos z dz in the numerator

74. anonymous

du = cos z dz, and you already have cos z dz in the numerator