anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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lgbasallote
  • lgbasallote
i believe the formula would be \[\large \frac{50!}{5! 45!}\] feel free to correct me though @apoorvk
anonymous
  • anonymous
where did you get the 45?
lgbasallote
  • lgbasallote
50 - 5 i believe

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More answers

ParthKohli
  • ParthKohli
Yes, it'd be 50c5 \(\Large \color{purple}{ 50! \over (50 - 5)!*5! }\)
ParthKohli
  • ParthKohli
Get it?
amorfide
  • amorfide
|dw:1337518895638:dw|
ParthKohli
  • ParthKohli
nCr is represented as: \(\Large \color{purple}{ {n! \over (n - r)!*r!} }\)
amorfide
  • amorfide
n= the amount of numbers =50 r= the numbers you want so 5 50!/(50-5)!5!
apoorvk
  • 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
  • lgbasallote
heh i cant believe i got the formula right..i only context clues-ed from amistre's work earlier \m/
ParthKohli
  • ParthKohli
If you have to choose 5 numbers from 50, then it'll be 50 choose 5 aka 50c5
lgbasallote
  • lgbasallote
can you go from there now @catgirl17
ParthKohli
  • ParthKohli
Considering that you know what factorials are lolz
amorfide
  • amorfide
oh god please know what factorials are...
lgbasallote
  • lgbasallote
it's gonna be a long post slash night if fno
ParthKohli
  • ParthKohli
\(\Large \color{purple}{ n! = n * (n - 1) * (n - 2) * (n - 3) ........1 }\)
anonymous
  • anonymous
after 50!/45!x5! do i just expand it out
ParthKohli
  • ParthKohli
Just having some fun
lgbasallote
  • lgbasallote
yes you do @catgirl17
ParthKohli
  • ParthKohli
And then you cancel to make it simpler.
lgbasallote
  • lgbasallote
and if i were you get rid of x...you might mistake it for a variable
anonymous
  • anonymous
thank you @lgbasallote
ParthKohli
  • ParthKohli
Use * instead of x lol
lgbasallote
  • lgbasallote
\[\huge \color{maroon}{\mathtt{\text{}}}\]
ParthKohli
  • ParthKohli
* doesn't only represent the thing that twinkles. lol
lgbasallote
  • lgbasallote
or use ( )( ) yeah...they're more subtle
ParthKohli
  • ParthKohli
\(\Large \color{purple}{\mathbb{Still} \text{ doesn't get the medal. xP} }\)
anonymous
  • anonymous
when expanding the 50! out do i have to go all the way to 5! ?
amorfide
  • amorfide
50! =50x49x48x47......x1
ParthKohli
  • ParthKohli
wait wait... n! OVER r! = (n - r)!
amorfide
  • amorfide
50!/45! cancels out to 50x49x48x47x46 divide that by 5!
lgbasallote
  • 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
  • amorfide
why have you got all those factorials on top?!
ParthKohli
  • ParthKohli
Are you kdding me? 50! is not 50! * 49!........
lgbasallote
  • lgbasallote
fine get rid of the ! :P
amorfide
  • amorfide
|dw:1337519562320:dw|
lgbasallote
  • lgbasallote
i just context clues-ed this topic sheesh
anonymous
  • anonymous
is the answer 50,850,240
ParthKohli
  • ParthKohli
n! What it really is ----> n * (n - 1) * (n - 2).......*1 What I think it is -------> n!!!!!!!!!!!!!!!!!!!
lgbasallote
  • lgbasallote
\[\large \frac{50 \times 49 \times 48 \times 47 \times 46 \times 45!}{45!5!}\] 45! cancels out
anonymous
  • anonymous
okay that's what i did
amorfide
  • amorfide
do it as a fraction on your scientific calculator
amorfide
  • amorfide
i get 2118760
ParthKohli
  • ParthKohli
\(\Large \color{purple} {{50 * 49 * 48 * 47 * 46 \over 5 * 4 * 3 * 2 } }\)
ParthKohli
  • ParthKohli
You need a calculator for this?!?!
amorfide
  • amorfide
i dont need one it is just quicker :P
lgbasallote
  • lgbasallote
2118760 it is
ParthKohli
  • ParthKohli
\(\Large \color{purple}{\mathbb{C}\mathbb{A}LCULATOR }\) FAIL.
anonymous
  • anonymous
how did ya'll get that answer cause im not getting that.
amorfide
  • amorfide
catgirl what are you putting into your calculator, tell us exactly
anonymous
  • anonymous
50x49x48x47x46/5
amorfide
  • amorfide
no it is not 5 it is 5!
amorfide
  • amorfide
5!=5x4x3x2x1
ParthKohli
  • ParthKohli
Lol no! The denominator would be 5 * 4 * 3 * 2
anonymous
  • anonymous
would someone just show me how you got your answer and all the steps to get there, please.
ParthKohli
  • ParthKohli
Just read all the replies again. You'll get what we did
amorfide
  • amorfide
|dw:1337520226834:dw|
amorfide
  • 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
  • amorfide
! means it is a factorial and a factorial is the number multiplied by every number before it

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