Mathematics, 16.01.2020 19:31 SophieCasey
If 6 cards are drawn at random from a standard deck of 52 cards, what is the probability that exactly 2 of the cards are spades?
Answers: 3
![n(S)=^{52}C_6=\dfrac{52!}{6!(52-6)!}=\dfrac{52\times51\times50\times49\times48\times46!}{6\times5\times4\times3\times2\times1\times46!}=20358520,\\\\\\n(A)\\\\\\=^{13}C_2\times^{39}C_4~~~~~~~~~~~~~~~~[\textup{there are 13 spades in the deck}]\\\\\\=\dfrac{13!}{2!(13-2)!}\times\dfrac{39!}{4!(39-4)!}\\\\\\=\dfrac{13\times12\times11!}{2\times1\times11!}\times\dfrac{39\times38\times37\times36\times35!}{4\times3\times2\times1\times35!}\\\\\\=78\times82251\\\\=6415578.](/tpl/images/0458/0004/08520.png)
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If 6 cards are drawn at random from a standard deck of 52 cards, what is the probability that exactl...
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