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Rogerio
#4
Feb15-09, 04:50 AM
P: 403
Probability- drawing cards from a deck.

Quote Quote by tiny-tim View Post
You have to count all the ways of drawing 10 cards...
[tex] {52\choose 10} [/tex]

Quote Quote by tiny-tim View Post
and all the ways in which 4 of them are the same.
Well, there are aces, kings, queens, jacks, etc...So,

#combinations we are interested in =
#combinations with 4 aces (including combinations with 4 kings, etc... )
PLUS
#combinations with 4 kings (including combinations with 4 aces, etc... )
PLUS
etc...
MINUS
#combinations with 4 aces e 4 kings (because they were counted twice )
MINUS
#combinations with 4 aces e 4 queens (because they were counted twice )
MINUS
etc...

That is:
[tex]{13\choose 1}{48\choose 6} - {13\choose 2}{44\choose 2}[/tex]



So, the probability of getting four of same rank is
[tex]\frac{{13\choose 1}{48\choose 6}-{13\choose 2}{44\choose 2}}{{52\choose 10}}=\frac{6483}{643195}[/tex]