## anonymous 3 years ago Evaluating expressions,

1. anonymous

Easiest problem ever, but I forgot how to do them, |dw:1361117139126:dw| Can someone show me step by step how to solve this or create a problem giving me an example? Thanks.!

2. anonymous

$1-\frac{ 694 }{ 896 }$ do you mean?

3. anonymous

No, its P

4. anonymous

then p4 do you mean its power or 4 is multiplied?

5. anonymous

like p4 or $p^4$

6. anonymous

I have no idea... It just says 6P4,

7. anonymous

Noo, its not that, I'll take a screenshot

8. anonymous

ok... i am waiting for screenshot.

9. anonymous

This is the problem,

10. anonymous

this is Permutation.

11. hartnn

ohh..its permutation!

12. anonymous

I also have this problem that includes a exclamation mark, |dw:1361117585779:dw| Do you know what its for?

13. anonymous

& whats permutation? O_O I have never ever heard of that

14. hartnn

$$!$$ means a factorial.

15. hartnn

$$n!= n(n-1)(n-2).......3.2.1$$ when n is a whole number. like for example 5! = 5*4*3*2*1 = 120

16. anonymous

answer is 1 it means that you need to expand 6 as 4 times and 8 as 6 times.

17. anonymous

1/56

18. hartnn

before getting to permutation, you should know what a factorial ! is .

19. anonymous

OH.! so I had something like 10! I would have to do 10*9*8*7*6*5*4*3*2*1= etc..?

20. hartnn

yes, thats correct.

21. anonymous

6P4= 6*5*4*3 and 8P6= 8*7*6*5*4*3

22. anonymous

yes you are correct.

23. hartnn

do you want to know how to get that^ ?

24. anonymous

I feel like I've done this stuff in 8th grade but had forgotten how to do some of this. These questions are for my pre-cal class & I found it odd that I had a probability question in there

25. anonymous

yes.

26. hartnn

$$\huge ^nP_r = \dfrac{n!}{(n-r)!}$$

27. anonymous

So basically I had to do the factorial (!) to the 6P & 8P?

28. anonymous

yes.

29. hartnn

$$\huge ^nP_r = \dfrac{n!}{(n-r)!} \\\huge ^6P_4 = \dfrac{6!}{(2)!} \\ \huge 8P_6 = \dfrac{8!}{(2)!}$$

30. anonymous

Everything on the left side of the = is confusing to me

31. hartnn

in the formula of nPr ? its just a formula, so for 6P4, i plugged in n=6 and r=4 in the standard formula.

32. anonymous

How would you know which ones to plug in? Because in one you have 6P4 & in the next 8P6, I don't get how you go to that?

33. hartnn

n is before P , r is after P . in 6P4 , 6 is before P (so, n=6) and 4 is after P (so r=4) does this makes sense ?

34. anonymous

Ah, it does now.! :-) Thanks you guys both for explaining this to me.!

35. hartnn

Thank me when you get to correct answer.

36. anonymous

What do you mean?

37. hartnn

i meant to ask you, whether you could now figure out the answer of that question...

38. anonymous

I do the factorial, 8*7*6*5*4*3*2*1, I thought?

39. anonymous

& then divide my answer by 2?

40. hartnn

thats for 8P2

41. anonymous

Then I'm lost again,

42. hartnn

i never said you are wrong. its just not the final answer.

43. anonymous

Then I do the same with the 6

44. hartnn

6P4 = 6*5*4*3 8P2= 8*7*6*5*4*3 Question asks, 1- 6P4/8P2 = 1- 6*5 / 8*7*6*5 = 1- 1/(8*7) ok ?

45. anonymous

Ah, I wasnt paying attention to the 1,

46. anonymous

Would I have to subtract the 1 from the 6 & start factoring 5?

47. hartnn

no... first division operation is performed, so 6*5*4*3 will get cancelled from numerator and denominator, and what remains is just 1- 1/(8*7) which i've already shown.

48. anonymous

Thats confusing

49. hartnn

ok, clear till this : 6P4 = 6*5*4*3 8P2= 8*7*6*5*4*3

50. anonymous

Got that...

51. hartnn

now divide them 6P4/8P2 =.... ?

52. anonymous

I got 0.0178 etc... Thats not right..

53. hartnn

keep it in fractions..

54. anonymous

I got 360 from 6*5*4*3 & 20160 from the factorial of 8.

55. anonymous

How would I keep it in fractions?

56. hartnn

you can also cancel out like this : |dw:1361120576575:dw| got that ?

57. anonymous

Ah, got it.! I wasnt thinking about canceling out

58. hartnn

59. anonymous

What happened to the 4 & 2?

60. hartnn

i just realized i mistyped 8P6 (and have written 8P2 instead) 4 and 2 where ?

61. anonymous

The 4 after the P and the 2 after the other P

62. hartnn

oh, we used the formula, right ? 6-4 = 2, so 2! in the denominator 8-6= 2, so 2! in the denominator

63. anonymous

OH.! Ok I get it.!

64. anonymous

1/56 wasnt correct, could it be 55/56 by any chance?

65. hartnn

?? you forgot '1-...' again ? 1- 1/(7*8)= 1-1/56=(56-1)/56 = 55/56

66. anonymous

*face palm* Thank you.

67. hartnn

welcome ^_^