A social insurance number (SIN) in Canada consists of a nine-digit number that uses the digits 0 to 9. How many SINs can be created if each digit can be repeated?

Use the given information to answer each question in the flowchart. Record your responses.

Flowchart Questions
Response
Explanation
Does order matter?
Yes
Various arrangements of the digits would result in different SINs.
Are you using all the objects in the group?
No
There is no requirement in the question that every digit be used.
Are some of the objects identical?
No
Each of the digits is distinct.
Are there conditions?
Yes
AND condition: Repetition means each digit can be used more than once.

Based on your responses in the chart above, you know to use n P r and multiplication.

The total number of SINs for these conditions is 1 000 000 000.

 

Without using n P r , you may have recognized intuitively that 10 would be placed for each task because this is a Fundamental Counting Principle problem.

 

Complete the question to practice solving permutations when repetition is allowed.

Hold your mouse over the question to verify your answer .

If you have any difficulty with the solution, please contact your teacher before continuing.