Q. What is the probability of getting a Royal Flush?

Ans.

Five cards are picked from a standard deck of 52 cards. How many different hands of five cards are possible? What is the probability of getting a Royal Flush?

Solution: We are choosing 5 objects, r = 5, from 52, n = 52, and we are not interested in the order in which they are picked. Thus, the number of different hands is

There are over 2 million possible hands!

A Royal Flush is a set of five cards: 10, Jack, Queen, King and Ace, all the same suit. Since there are 4 suits, there are only 4 possible Royal Flush hands. Thus,

That is very small! The length of a typical bacterium is about , the same order of magnitude!