Question

A certain organization recommends the use of passwords with the following​ format: vowel commavowel, consonant comma consonant comma consonant comma vowel comma consonant comma number comma numberconsonant, consonant, consonant, vowel, consonant, number, number ​(for example, inpray 93inpray93​). 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

The password format is = inpray93

vowel , consonant, consonant, consonant, vowel, consonant, number, number.

There are 21 consonants, 5 vowels and 10 number choices (0-9)

Since, there are 21 consonants and repetition is allowed so for 2nd, 3rd, 4th, and 6th positions 21 choices are available. For 1st and 5th positions, 5 choices  are available and for 7th and 8th position there are 10 choices (0 to 9).

Passwords are not case sensitive which means upper case and lower case letters are same.

So, the number of passwords can be =

$5\times21\times21\times21\times5\times21\times10\times10$

= 486202500

Part (b) question is not given. But it can be opposite to the first part i.e when the password letters are case sensitive.

This means all the letters are different.

So, number of passwords will be =

$10\times42\times42\times42\times10\times42\times10\times10$

= 31116960000