Answer:
36⁷- 26⁷ = 70332353920 passwords.
Step-by-step explanation:
Number of digits 0-9 = 10
Number of lowercase letters a-z = 26
We have to find different passwords of length 7 that contain only digits and lower-case letters.
Total number of characters = 26 lowercase letters + 10 digits
= 36
The total number of length 7 passwords without restrictions = 36⁷
= 78364164096
The number of length 7 passwords with no digits (only lowercase letters)
= 26⁷
= 8031810176
Now the restriction here is that the password must contain at least 1 digit. This can be computed by subtracting the number of length 7 passwords with no digits from total number of length 7 passwords.
Number of length 7 passwords with restriction (at least one digit) = 36⁷- 26⁷
= 36⁷- 26⁷
= 78364164096 - 8031810176
= 70332353920
So the number of different passwords that contain only digits and lower-case letters and satisfy the given restrictions that length is 7 and the password must contain at least one digit = 70332353920
