## catgirl17 3 years ago the kentucky lottery is worth \$100,000. to win you have to select the 5 winning numbers from 1-50. how many different combinations are possible?

1. lgbasallote

i believe the formula would be $\large \frac{50!}{5! 45!}$ feel free to correct me though @apoorvk

2. catgirl17

where did you get the 45?

3. lgbasallote

50 - 5 i believe

4. ParthKohli

Yes, it'd be 50c5 $$\Large \color{purple}{ 50! \over (50 - 5)!*5! }$$

5. ParthKohli

Get it?

6. amorfide

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7. ParthKohli

nCr is represented as: $$\Large \color{purple}{ {n! \over (n - r)!*r!} }$$

8. amorfide

n= the amount of numbers =50 r= the numbers you want so 5 50!/(50-5)!5!

9. apoorvk

no @lgbasallote I won't need to correct you. For choosing 'r' things out 'n', (arrangement not being considered), no. of possible combinations 'N': $\large N = ^nC_r = \frac{n!}{r!(n-r)!}$

10. lgbasallote

heh i cant believe i got the formula right..i only context clues-ed from amistre's work earlier \m/

11. ParthKohli

If you have to choose 5 numbers from 50, then it'll be 50 choose 5 aka 50c5

12. lgbasallote

can you go from there now @catgirl17

13. ParthKohli

Considering that you know what factorials are lolz

14. amorfide

oh god please know what factorials are...

15. lgbasallote

it's gonna be a long post slash night if fno

16. ParthKohli

$$\Large \color{purple}{ n! = n * (n - 1) * (n - 2) * (n - 3) ........1 }$$

17. catgirl17

after 50!/45!x5! do i just expand it out

18. ParthKohli

Just having some fun

19. lgbasallote

yes you do @catgirl17

20. ParthKohli

And then you cancel to make it simpler.

21. lgbasallote

and if i were you get rid of x...you might mistake it for a variable

22. catgirl17

thank you @lgbasallote

23. ParthKohli

Use * instead of x lol

24. lgbasallote

$\huge \color{maroon}{\mathtt{\text{<tips hat>}}}$

25. ParthKohli

* doesn't only represent the thing that twinkles. lol

26. lgbasallote

or use ( )( ) yeah...they're more subtle

27. ParthKohli

$$\Large \color{purple}{\mathbb{Still} \text{ doesn't get the medal. xP} }$$

28. catgirl17

when expanding the 50! out do i have to go all the way to 5! ?

29. amorfide

50! =50x49x48x47......x1

30. ParthKohli

wait wait... n! OVER r! = (n - r)!

31. amorfide

50!/45! cancels out to 50x49x48x47x46 divide that by 5!

32. lgbasallote

just until 45! it will cancel out anyway... $\large \frac{50! 49! 48! 47! 46! 45!}{45! 5!}$ see? 45! will just cancel out

33. amorfide

why have you got all those factorials on top?!

34. ParthKohli

Are you kdding me? 50! is not 50! * 49!........

35. lgbasallote

fine get rid of the ! :P

36. amorfide

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37. lgbasallote

i just context clues-ed this topic sheesh

38. catgirl17

39. ParthKohli

n! What it really is ----> n * (n - 1) * (n - 2).......*1 What I think it is -------> n!!!!!!!!!!!!!!!!!!!

40. lgbasallote

$\large \frac{50 \times 49 \times 48 \times 47 \times 46 \times 45!}{45!5!}$ 45! cancels out

41. catgirl17

okay that's what i did

42. amorfide

do it as a fraction on your scientific calculator

43. amorfide

i get 2118760

44. ParthKohli

$$\Large \color{purple} {{50 * 49 * 48 * 47 * 46 \over 5 * 4 * 3 * 2 } }$$

45. ParthKohli

You need a calculator for this?!?!

46. amorfide

i dont need one it is just quicker :P

47. lgbasallote

2118760 it is

48. ParthKohli

$$\Large \color{purple}{\mathbb{C}\mathbb{A}LCULATOR }$$ FAIL.

49. catgirl17

how did ya'll get that answer cause im not getting that.

50. amorfide

catgirl what are you putting into your calculator, tell us exactly

51. catgirl17

50x49x48x47x46/5

52. amorfide

no it is not 5 it is 5!

53. amorfide

5!=5x4x3x2x1

54. ParthKohli

Lol no! The denominator would be 5 * 4 * 3 * 2

55. catgirl17

would someone just show me how you got your answer and all the steps to get there, please.

56. ParthKohli

Just read all the replies again. You'll get what we did

57. amorfide

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58. amorfide

n=50 because the over all amount of numbers you have are 50 numbers r=5 because you want a specific 5 from the 50 numbers you have combination means the order of numbers do not matter aslong as you have the numbers there they count as a combination (different to permutations) so the formula is n!/(n-r)!r! sub in

59. amorfide

! means it is a factorial and a factorial is the number multiplied by every number before it