15 consonant and 4 vowels how many strings of 4 letter 1 exa

15 consonant and 4 vowels. how many strings of 4 letter:

1. exactly 1 vowel (repeats allowed)
2. at most 1 vowel (repeats allowed)
3. at most 3 vowels (no repeats)

Solution

1) . exactly 1 vowel (repeats allowed)

there are 4 ways to select a letter from 4 vowels

now we have to form 3 letter string from 15 consonants

number of ways=15*15*15 since repetition of letters allowed

there total number of strings=4*15*15*15