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)?

 (a). Passwords = 48620250

               (b). Passwords = 3111696000

Step-by-step 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

the correct answer is x/3+10≥32

hope this !