Answer: [tex]\dfrac{9}{66892280}[/tex]
Step-by-step explanation:
Number of combinations of r things from n things = [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
Number of combinations of choosing 9 cards out of 52 = [tex]^{52}C_9=\dfrac{52!}{9!(52-9)!}=3679075400[/tex]
Total face cards = 12
Number of combinations of choosing 8 face cards = [tex]^{12}C_8=\dfrac{12!}{8!(12-8)!}=495[/tex]
Required probability = [tex]\dfrac{495}{3679075400}=\dfrac{9}{66892280}[/tex]
Hence, the probability that the hand contains exactly 8 face cards. = [tex]\dfrac{9}{66892280}[/tex]
