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