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?

- anonymous

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- lgbasallote

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

- anonymous

where did you get the 45?

- lgbasallote

50 - 5 i believe

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## More answers

- ParthKohli

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

- ParthKohli

Get it?

- amorfide

|dw:1337518895638:dw|

- ParthKohli

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

- amorfide

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

- 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':
\[\large N = ^nC_r = \frac{n!}{r!(n-r)!}\]

- lgbasallote

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

- ParthKohli

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

- lgbasallote

can you go from there now @catgirl17

- ParthKohli

Considering that you know what factorials are lolz

- amorfide

oh god please know what factorials are...

- lgbasallote

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

- ParthKohli

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

- anonymous

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

- ParthKohli

Just having some fun

- lgbasallote

yes you do @catgirl17

- ParthKohli

And then you cancel to make it simpler.

- lgbasallote

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

- anonymous

thank you @lgbasallote

- ParthKohli

Use * instead of x lol

- lgbasallote

\[\huge \color{maroon}{\mathtt{\text{}}}\]

- ParthKohli

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

- lgbasallote

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

- ParthKohli

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

- anonymous

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

- amorfide

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

- ParthKohli

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

- amorfide

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

- 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

- amorfide

why have you got all those factorials on top?!

- ParthKohli

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

- lgbasallote

fine get rid of the ! :P

- amorfide

|dw:1337519562320:dw|

- lgbasallote

i just context clues-ed this topic sheesh

- anonymous

is the answer 50,850,240

- ParthKohli

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

- lgbasallote

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

- anonymous

okay that's what i did

- amorfide

do it as a fraction on your scientific calculator

- amorfide

i get 2118760

- ParthKohli

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

- ParthKohli

You need a calculator for this?!?!

- amorfide

i dont need one it is just quicker :P

- lgbasallote

2118760 it is

- ParthKohli

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

- anonymous

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

- amorfide

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

- anonymous

50x49x48x47x46/5

- amorfide

no it is not 5 it is 5!

- amorfide

5!=5x4x3x2x1

- ParthKohli

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

- anonymous

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

- ParthKohli

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

- amorfide

|dw:1337520226834:dw|

- 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

- amorfide

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

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