A certain organization recommends the use of passwords with the following format:
consonant comma
consonant,
consonant comma vowel comma consonant comma vowel comma consonant comma number comma number
consonant, vowel, consonant, vowel, consonant, number, number (for example,
prinay 67
prinay67). Assume that repeats are allowed. Complete parts (a) and (b).
(a) Assuming passwords are not case sensitive, how many such passwords are possible (assume that there are 5 vowels and 21 consonants)?
(Simplify your answer.)
To find the number of possible passwords using the given format, we need to determine the number of choices for each part of the format.
(a) The format consists of 7 parts: consonant, comma, consonant, vowel, comma, consonant, vowel, comma, consonant, comma, number, comma, number.
For the first part (consonant), there are 21 choices since there are 21 consonants.
For the second part (comma), there is only 1 choice.
For the third part (consonant), there are 21 choices.
For the fourth part (vowel), there are 5 choices since there are 5 vowels.
For the fifth part (comma), there is only 1 choice.
For the sixth part (consonant), there are 21 choices.
For the seventh part (vowel), there are 5 choices.
For the eighth part (comma), there is only 1 choice.
For the ninth part (consonant), there are 21 choices.
For the tenth part (comma), there is only 1 choice.
For the eleventh part (number), there are 10 choices since there are 10 digits (0-9).
For the twelfth part (comma), there is only 1 choice.
For the thirteenth part (number), there are 10 choices again.
To find the total number of possible passwords, we multiply the number of choices for each part together:
Total number of possible passwords = 21 * 1 * 21 * 5 * 1 * 21 * 5 * 1 * 21 * 1 * 10 * 1 * 10
Simplifying the expression:
Total number of possible passwords = 21 * 21 * 21 * 5 * 5 * 10 * 10
Total number of possible passwords = 2,310,750
Therefore, there are 2,310,750 possible passwords using the given format (assuming passwords are not case sensitive).
To find the number of possible passwords, we need to calculate the total number of options for each position in the password.
(a) Assuming passwords are not case sensitive, we have the following format for the password:
1. Consonant,
2. Consonant,
3. Consonant, Vowel, Consonant, Vowel, Consonant, Number, Number.
Let's break it down for each position:
1. Consonant (comma) - There are 21 consonants, so there are 21 options.
2. Consonant - Again, there are 21 consonants, so 21 options.
3. Consonant, Vowel, Consonant, Vowel, Consonant, Number, Number - In this sequence, we have:
(a) Consonant - 21 options
(b) Vowel - 5 options
(c) Consonant - 21 options
(d) Vowel - 5 options
(e) Consonant - 21 options
(f) Number - 10 options (0-9)
(g) Number - 10 options (0-9)
To find the total number of possible passwords, we need to multiply the number of options for each position together:
Total number of passwords = (21) * (21) * (21) * (5) * (21) * (5) * (21) * (10) * (10)
Simplifying this expression:
Total number of passwords = 4,808,025,000
It would help if you proofread your questions before you posted them.
No part (b).
(a) With repeats allowed, multiply all consonants by 21, all vowels by 5 and all numbers by 10 to get the total number of passwords possible.