Question

Of the 2,598,960 different five-card hands possible from a deck of 52 playing cards, how many would contain all black cards.

Answer 1

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 = $^nC_r=\dfrac{n!}{(n-r)!r!}$

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 = $^{26}C_{5}=\dfrac{26!}{(26-5)!5!}$

$=\dfrac{26\times25\times24\times23\times22\times21!}{21!(120)}=65780$

Hence, the number of different five-card hands possible from a deck of 52 playing cards such that all are black cards = 65,780