College Algebra, Chapter 10, Review Exercises, Section Review Exercises, Problem 32

In the "numbers game" lottery a player picks a three-digit number (from 000 to 999), and if the number is selected in the drawing, the player wins $\$ 500$. If another number with the same digits (in any order) is drawn, the player wins $\$ 50$. John plays the number 159.

a.) What is the probability that he will win $\$ 500$?

There are 1000 possible three-digit numbers to select from 000-999. In which, only one of these is the correct arrangement. Thus, the probability in this case is

$\displaystyle \frac{1}{1000} = 0.001$

b.) What is the probability that he will win $\$ 50$?

Since the order in this problem is not important, then there are $3!$ ways to arrange this number. However, if the correct arrangement has already been chosen, then there will be only $3!-1$ ways to win the $\$ 50$. Thus, the probability in this case is

$\displaystyle \frac{3! -1}{1000} = \frac{1}{200} = 0.005$