Question

Ron forgot the password of an online service, but remembers that the password was just made of lowercase vowels (a, e, i ,o, u), was 4 characters long and contained at least one 'a'. How many possible passwords fulfill these requisites?

Answer 1

Solution :

Password is 4 characters long. The password was made of lowercase vowels and contained at least one a.

So we have four places to fill with five characters (a, e, i, o, u).

Total number of possible passwords :

At each of the four places any of the 5 characters can appear. Hence, total number of possible passwords is given by,

Total = (5 × 5 × 5 × 5) = 625

Number of possible passwords without the character "a" :

If "a" is excluded from the vowels, then we are left with 4 vowels (e, i, o, u). At each of the four places any of the four remaining vowel character can appear. Hence, Number of possible passwords without the character "a is given by,

Without "a" = (4 × 4 × 4 × 4) = 256

Hence, number of possible passwords with lower case vowels such that it contains at least one "a" is given by,

Required number = Total - Without "a"

Required number = 625 - 256

Required number = 369

Hence, there are 369 possible passwords that full fill the requisites.