Answer to Question #241201 in Statistics and Probability for Lynn

Question #241201

Five cards are drawn from a pack of 52 well-shuffled cards. Find the probability that the 4 cards are aces AND 1 card is a king. 


1
Expert's answer
2021-09-24T01:01:12-0400

There are 4 aces and 4 kings in a standard deck of 52 cards.

Then


P(4 Aces & 1 King)=(44)(41)(525)P(4\ Aces\ \&\ 1\ King)=\dfrac{\dbinom{4}{4}\dbinom{4}{1}}{\dbinom{52}{5}}

=1(4)52!5!(525)!=4(120)52(51)(50)(49)(48)=\dfrac{1(4)}{\dfrac{52!}{5!(52-5)!}}=\dfrac{4(120)}{52(51)(50)(49)(48)}

=16497400.00000154=\dfrac{1}{649740}\approx0.00000154



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