Answer:
1. 2,821,109,907,456 passwords
2. 2,612,282,842,880 passwords
3. 0.93
Step-by-step explanation:
Number of lower case letters = 26
Number of digits = 10
Total Characters = 26 + 10 = 36
Length of password = 8
1. Each character can be chosen from 36 objects (26 lowercase letters and 10 digits).
Since there's no restriction on repetition of characters, there are
(26+10)^8 different passwords
= 36^8
= 2,821,109,907,456 passwords
2.
For atleast one character to be a must be a digit means 1 character or 2 character or 3 characters... and so on
So we calculate by looking at no character being a digit
and then subtract the result from the total(36^8).
No character being a digit = All the characters are only letters
I.e. 26^8
Atleast one character being a digit = 36^8 - 26^8
= 2,821,109,907,456 - 208,827,064,576
= 2,612,282,842,880 passwords
3.
Probability = Number of possible outcomes/Number of Total outcomes
Number of possible outcomes = Number of Atleast 1 digit = 36^8 - 26^8 (as in question 2)
Total outcomes = 36^8
Probability = (36^8 - 26^8) / 36^8
= 2,612,282,842,880 / 2,821,109,907,456
= 0.92597698373108952
= 0.93 (approximated)
