The Situation
Imagine you are creating a personal identification number (PIN) using four numbers from the set 0 to 9, including 0 and 9. Once a number is used, it cannot be reused. In this scenario, how many possible outcomes exist?
Total Possible Outcomes
There are 10 choices for the first number, 9 choices for the second (since one number has been used), 8 choices for the third, and 7 choices for the fourth. Therefore, the total possible outcomes can be calculated as 10 x 9 x 8 x 7 = 5,040.
Outcomes Beginning with 0
When it comes to outcomes that begin with 0, we have 9 choices for the first number (excluding 0), 9 choices for the second, 8 choices for the third, and 7 choices for the fourth. Therefore, the total possible outcomes that begin with 0 can be calculated as 9 x 9 x 8 x 7 = 3,024.
Conclusion
Creating a four-number PIN from the set 0 to 9 provides a multitude of possibilities. With 5,040 total outcomes and 3,024 outcomes beginning with 0, individuals have the flexibility to choose a unique and secure PIN that suits their preferences.
