3. We want to require users to enter a password to access our new application bu

Question

3. We want to require users to enter a password to access our new application but we haven't decided the format of the password. For each of the following format options, assume that order matters. The characters include 26 lower case letters, 26 upper case letters and 10 digits. Count the number of unique passwords generated by each of the following password formats. a. A password consists of 6 digits. No repetition is allowed b. A password consists of 6 characters. The first can be any character. The second can be any character except an X, Y, 0 or 1. The next 4 characters are all digits. Repetition is allowed.

Explanation / Answer

1) The password contains 6 digits: no repetition
Hence at first place, there can be any digit out of 0 to 9 => 10 choices.
At second place: Any digit out of 0 to 9 but not what has been selected in the first step.. SO => 9 choices
At third place => 8 choices..
and so on..

So total unique passwords generated = 10 * 9 * 8 * 7 * 6 * 5
= 151200 passwords

2) Password contains 6 characters.. There are total of 26+26+10=62 characters available
As repetition is allowed, whatever we choose at some particular place, doesn't make any difference for other positions
So at first place => 62 choices
at second place: 62 - 4 characters => 58 choices
at third place: only 10 characters out of digit => 10 choices
at fourth place: only 10 characters out of digit => 10 choices
at fifth place: only 10 characters out of digit => 10 choices
at sixth place: only 10 characters out of digit => 10 choices

So total count = 62 * 58 * 10 * 10 * 10 * 10 = 35960000

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.