Question

The inhabitants of the island of jumble use the standard kobish alphabet ($20$ letters, a through t). each word in their language is $4$ letters or less, and for some reason, they insist that all words contain the letter a at least once. how many words are possible?

Answer 1

We know that

1. The number of all 4-letter words written using the alphabet of 20 symbols (from A to T) is 
20^4=160,000

 2. The number of all 4-letter words written using the alphabet of 19 symbols (from B to T) is 
19^4=130,321

 3. The difference represents exactly the number of all words of the inhabitants of the island of Jumble
difference=(160,000-130,321)= 29679.

the answer is
29679