College Algebra & Trigonometry, 2018a

308 CHAPTER 7. COMBINATORICS
Example:
In many states the license plates for automobiles consist of three letters followed
three numbers.
How many different possibilities are there:
if repetition of letters and numbers is allowed?
if repetition of letters and numbers is not allowed?
There are six positions for letters and numbers that make up the license plate.
The first three are to be letters and the second three numbers.
There are 26 choices for the first three and 10 choices for the second three, so there
are 26 ∗ 26 ∗ 26 ∗ 10 ∗ 10 ∗ 10 = 17, 576, 000 possible license plates if repetition is
allowed.
If repetition is not allowed then we have to discount whichever letter or number
is chosen for a particular position. So, for the first letter there are 26 possibilities,
but then only 25 for the second letter and 24 for the third. Likewise, with the
numbers there are 10 choices initially, then 9 choices and then 8.
So, the solution without repetition would be 26 ∗ 25 ∗ 24 ∗ 10 ∗ 9 ∗ 8=11, 232, 000