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Step-by-step explanation:
5 cards are drawn.
"more than 4" means then exactly 5.
a probability is always
desired cases / total possible cases
we have 14 red cards and 6 black cards. in total 20 cards.
how many patterns of 5 cards are possible in total ?
that are 20 over 5 combinations :
20! / (5! × (20-5)!) = 20×19×18×17×16/(5×4×3×2) =
= 4×19×6×17×4/2 = 2×19×6×17×4 =
= 15,504 total cases
the desired cases of more than 4 red cards (= 5 red cards) is 6 over 5 combinations (how many ways to pull 5 cards out of 6 red cards) :
6! / (5! × (6-5)!) = 6
so, the probability for that is
6 / 15,504 = 1/2,584 = 0.0003869969...