immanuelv
  • immanuelv
if you draw a 5-card hand from a standard deck of playing cards, how many hands could contain exactly 4 cards from the same suit?
Mathematics
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
wait a little confused. does this mean what is the probability you get exactly 4 cards of the same suit?
anonymous
  • anonymous
watchmath do you understand this question?
anonymous
  • anonymous
perhaps the answer is \[\dbinom{13}{4}\times \dbinom{39}{1}\times 4\]?

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anonymous
  • anonymous
i don't really know how to intemperate "if you draw a 5-card hand"..."how many hands"
immanuelv
  • immanuelv
that is what i'm trying to figure out!
anonymous
  • anonymous
well maybe it means how many possible hand have 4 of one suit and two of another. if so, lets start with clubs. you need 4 clubs and 1 non club. the number of ways to get 4 clubs is \[\dbinom{13}{4}\] and the number of ways you can choose one non-club is \[\dbinom{39}{1}\]
anonymous
  • anonymous
then we do the same for each other suit hence multiply by 4
immanuelv
  • immanuelv
yes.....
immanuelv
  • immanuelv
my theory is 4(13 C4* 39C1)
anonymous
  • anonymous
that is what i wrote so it looks good to me
anonymous
  • anonymous
4*13*11*5*39
immanuelv
  • immanuelv
Thank you very much !!
anonymous
  • anonymous
welcome

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