Suppose a contest offers $1000 to the person who can guess the winning four digit number. How many possibilities are there?
There are two methods:
Method 1.
There are 9999 integers from 1 to 9999, inclusive.
There are 999 integers from 1 to 999, inclusive,
which are not four-digit numbers.
Subtracting: 9999 - 999 = 9000
Method 2.
There are 9 choices for the first digit (We cannot choose 0)
There are 10 choices for the second digit. (We CAN choose 0)
There are 10 choices for the third digit. (We CAN choose 0)
There are 10 choices for the fourth digit. (We CAN choose 0)
That's 9*10*10*10 = 9000.
Either way, you get 9000.
So he has one chance in 9000 to choose the right one.
Edwin