In: Statistics and Probability
An 8-character password consists of four numbers (from 1 to 9) followed by two letters (from A to Z) followed by two more numbers (from 1 to 9).
a) How many different passwords can be formed if letters and numbers can be repeated?
b) How many different passwords can be formed that have no repeated number or letters?
Solution:
We are given that: An 8-character password consists of four numbers (from 1 to 9) followed by two letters (from A to Z) followed by two more numbers (from 1 to 9).
Part a) How many different passwords can be formed if letters and numbers can be repeated?
We have 9 digits from 1 to 9 , 26 letters from A to Z.
We have to make 8 character password, such that letters and numbers can be repeated.
So we have total number of ways=
9 | 9 | 9 | 9 | 26 | 26 | 9 | 9 |
First four places are filled with digits and each place can be filled in 9 different ways, followed by next two places can be filled byletters and each of these places filled by 26 different ways and followed by last two places can be filled by 9 different ways for digits.
Thus
Total ways = 9 x 9 x 9 x 9 x 26 x 26 x 9 x 9
Total ways = 359254116
Part b) How many different passwords can be formed that have no repeated number or letters?
Here condition is no repetition of letters or numbers.
Thus we have to decrease number of digits for each next place by 1.
Thus for first place we have 9 ways , for second place we have 8 ways , for third we have 7 ways ,for foruth digit place we have 6 ways , followed by fornext two letters we have 26 ways and 25 ways respectively.
for last two places , we have 5 ways and 4 ways respectively.
9 | 8 | 7 | 6 | 26 | 25 | 5 | 4 |
Thus
Total Ways = 9 x 8 x 7 x 6 x 26 x 25 x 5 x 4
Total Ways = 39312000