Question

Fred randomly draws 2 cards from a standard deck of 52 cards. he does not replace the first card, what is the probability that both cards are queens

Answer 1

$\displaystyle |\Omega|=\binom{52}{2}=\dfrac{52!}{2!50!}=\dfrac{51\cdot52}{2}=1326\\ |A|=\binom{4}{2}=\dfrac{4!}{2!2!}=\dfrac{3\cdot4}{2}=6\\\\ P(A)=\dfrac{6}{1326}=\dfrac{1}{221}\approx0.5\%$

Answer 2

Total number of cards = 52

Total number of queens = 4

$P( \text {Both cards are queen} ) = \dfrac{4}{52} \times \dfrac{3}{51} = \dfrac{1}{221}$

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Answer: 1/221