Each character in a password is either a digit [0-9] or lowercase letter [a - z]. How many valid passwords are there with the given restriction(s)? Length is 12. No character repeats. Must contain: g Ex: P(11, 4) * P(4,3) Write permutations as: P(n, k)
Each character in a password is either a digit [0-9] or lowercase letter [a - z]. How many valid passwords are there with the given restriction(s)? Length is 12. No character repeats. Must contain: g Ex: P(11, 4) * P(4,3) Write permutations as: P(n, k)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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![### Password Restrictions and Calculations
Each character in a password is either a digit \([0 - 9]\) or a lowercase letter \([a - z]\). How many valid passwords are there with the given restriction(s)?
- **Length is 12.**
- **No character repeats.**
- **Must contain the character 'g'.**
#### Example:
Use permutations to calculate: \( P(11, 4) \times P(4, 3) \)
Write permutations as: \( P(n, k) \)
In this example, permutations are used to determine the number of ways to arrange characters under certain conditions. The notation \( P(n, k) \) represents the number of permutations of \( n \) items taken \( k \) at a time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb47bac88-cba5-40e5-9f3f-db7316eb95a3%2Fcad30ada-0908-4c32-a220-8d04feb706c6%2Fchcvbf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Password Restrictions and Calculations
Each character in a password is either a digit \([0 - 9]\) or a lowercase letter \([a - z]\). How many valid passwords are there with the given restriction(s)?
- **Length is 12.**
- **No character repeats.**
- **Must contain the character 'g'.**
#### Example:
Use permutations to calculate: \( P(11, 4) \times P(4, 3) \)
Write permutations as: \( P(n, k) \)
In this example, permutations are used to determine the number of ways to arrange characters under certain conditions. The notation \( P(n, k) \) represents the number of permutations of \( n \) items taken \( k \) at a time.
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