SOLUTION: three cards are drawn from a well shuffled deck. what is the probability that : a) all are black ? b) exactly one is a diamond ? c) all are hearts ?

SOLUTION: three cards are drawn from a well shuffled deck. what is the probability that : a) all are black ? b) exactly one is a diamond ? c) all are hearts ?

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Question 588430: three cards are drawn from a well shuffled deck. what is the probability that :
a) all are black ?
b) exactly one is a diamond ?
c) all are hearts ?
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
Assuming the deck has 52 cards.
Combination=nCr=n!/((n-r!)*r!)
a)
26 cards are black
(26C3)/(52C3) = 2/17
.
b)
13 cards are diamonds and 39 cards are non diamonds.
((13C1)(39C2))/52C3 = 741/1700
.
c)
13C3/52C3 = 11/850
.
Ed
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