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

Explanation:

When we select r things from n things , we use combinations and the number of ways to select r things =
`^nC_r=(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)=(26!)/((26-5)!5!)`

`=(26*25*24*23*22*21!)/(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