Answer:
Part b: The number of ways in which there will be four aces is 1677106641
Part c: The number of ways in which there will be at least one ace is 442085310304
Part d: The number of ways in which cards can be dealt is 635013559600
Step-by-step explanation:
Part b
The number of different bridge hands with four aces is
As Total Number of Hands with 4 aces is given as
As the order does not matter, thus the number of Hands with 4 aces is given as
[tex]n_{aces}=^{4}C_{4}+^{48}C_{9}=\frac{4!}{4!(4-4)!}+\frac{48!}{9!(48-9)!}\\n_{acesl}=\frac{4!}{4!(0)!}+\frac{48!}{9!(39)!}\\\\n_{aces}=1677106641[/tex]
So the number of ways in which there will be four aces is 1677106641
Part c
Total cards without ace = 48
Number of hands of (no ace) = [tex]n_{no aces}=48C13=192928249296[/tex]
Number of hands of (at least one ace)
[tex]n_{total} - n_{no-aces} \\= 635013559600-192928249296 \\= 442085310304[/tex]
So the number of ways in which there will be at least one ace is 442085310304
Part d
As Total Number of Hands is given as
Total Cards=52
Cards per Player=13
As the order does not matter, thus the number of Hands is given as
[tex]n_{total}=^{52}C_{13}=\frac{52!}{13!(52-13)!}\\n_{total}=^{52}C_{13}=\frac{52!}{13!(39)!} \\n_{total}=^{52}C_{13}=635013559600\\[/tex]
So the number of ways in which cards can be dealt is 635013559600
