Question

A certain organization recommends the use of passwords with the following​ format: consonant commaconsonant, consonant comma vowel comma consonant comma vowel comma consonant comma numberconsonant, vowel, consonant, vowel, consonant, number ​(for example, prinay 6prinay6​). 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)?

Answer 1

Answer: (a). Passwords = 48620250

(b). Passwords = 3111696000

Explanation:

The question reads that 'A certain organization recommends the use of passwords with the following format':

Consonant, Vowel, Consonant, Consonant, Vowel, Consonant, Number, Number (for example, pinray45​).

The number of consonants is 21, the number of vowels is 5 and the numbers are 10 (0 to 9).

Since, there are 21 consonants and 5 vowels and repetition is allowed.

Use the general multiplication rule for each characters in the sequence.

Multiply by 21 consonants, 5 for vowels and 10 for numbers.

Assuming that the passwords are not case sensitive.

i.e. upper case & lower case letters are same.

Thus, the number of possible passwords is:

Passwords = Consonant * Vowel * Consonant * Consonant * Vowel * Consonant * Number * Number

Passwords = 5 x 21 x 21 x 21 x 5 x21 x 10 = 48620250

(b). Assuming that the passwords are case sensitive

Passwords = 10 x 42 x 42 x 42 x 10 x 42 x 10 = 42 x 420³ = 3111696000

cheers i hope this helps!!!!