Q22. - Algebra 2

Question

Abby is registering at a Web site. She must select a password containing 6 numerals to be able to use the site. How many passwords are allowed if no digit may be used more than once?

Step-by-Step Solution

Answer

There are 151200 passwords allowed if no digit may be used more than once.

Step 1. Given Information.

Abby is registering at a Web site. She must select a password containing 6 numerals to be able to use the site. It is to be determined how many passwords are allowed if no digit may be used more than once.

Step 2. Calculation .

There are a total of 10 digits i.e., 0 to 9 and 6 places in the password.

When one of the digit is used in first place, 9 remain to be listed in the next place, then 8, then 7, then 6 and finally 5.

By the Fundamental Counting Principle, there are $10\times 9\times 8\times 7\times 6\times 5=151200$ different arrangements for 6 numerals using 10 digits.

Step 3. Conclusion .

Hence, by Fundamental Counting Principle, there are 151200 passwords allowed if no digit may be used more than once.