A certain organization recommends the use of passwords with the following format:

 (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

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