SOLUTION: A set of 8 cards contains 1 joker. A and B are 2 players and A chooses 5 cards at random, B taking the remaining 3 cards. What is the probability that A has the joker?

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Question 1086356: A set of 8 cards contains 1 joker. A and B are 2 players and A chooses 5 cards at random, B taking the
remaining 3 cards. What is the probability that A has the joker?

Found 2 solutions by Edwin McCravy, Fombitz:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

If A has the joker, there are 7C4 ways he could have the other 4 
non-jokers.  So 7C4 is the numerator of the probability.

There are 8C5 ways he could have any 5 cards.  So 8C5 is the denominator 
of the probability.

Answer: 7C4%2F%288C5%29=35%2F56=5%2F8

Edwin

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
There are 56 possible combinations choosing 5 cards out of 8 total (A,B,C,D,E,F,G,J) where J is the joker.
There are 21 possible combinations choosing 5 cards out of 7 total.
(A,B,C,D,E,F,G) where there is no joker.
So in 21 of the 56 outcomes, the joker is in the B hand.
So in the A hand,
P=35%2F56=5%2F8