A) \[\frac{6}{4165}\]
B) \[\frac{4}{4165}\]
C) \[\frac{3}{4165}\]
D) None of these
Correct Answer: A
Solution :
[a] There are 6 ways to select 2 cards of the same kind from the 4 cards in the deck and there are 13 different kinds of cards, so the total number of combinations possible of 2 cards is \[6\times 13=78.\]There are 4 ways to choose 3 cards of the same kind from 4 cards of the same kind, but because the 3-of a-king suit must be different from the 2-of -a-kind suit, the possible combinations of this is, \[4\times 12=48.\] So total number of ways is \[=48\times 78=3744\] Sample space is \[^{52}{{C}_{5}}=2,598,560\] Required probability \[=\frac{3744}{2598560}=\frac{6}{4165}\]
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