Answer: 65,780
Step-by-step explanation:
When we select r things from n things , we use combinations and the number of ways to select r things = [tex]^nC_r=\dfrac{n!}{(n-r)!r!}[/tex]
Given : The total number of playing cards in a deck = 52
The number of different five-card hands possible from a deck = 2,598,960
In a deck , there are 26 black cards and 26 red cards.
The number of ways to select 5 cards from 26 cards = [tex]^{26}C_{5}=\dfrac{26!}{(26-5)!5!}[/tex]
[tex]=\dfrac{26\times25\times24\times23\times22\times21!}{21!(120)}=65780[/tex]
Hence, the number of different five-card hands possible from a deck of 52 playing cards such that all are black cards = 65,780
