The inhabitants of the island of Jumble use the standard Roman alphabet (26 letters, A through Z). Each word in their language is 3 letters, and for some reason, they insist that all words contain the letter A at least once. How many 3-letter words are possible?

gueesstt Apr 22, 2018

#1**+1 **

The A can appear in any one of 3 positions when it is used once

And there are 25 * 25 posiibilities for the other two positions

So..... C( 3, 1) * 25^2 = 1875

When the word has 2 A's....they can appear in any two of the three positions

And the the other position can be filled in 25 ways

So C(3,2) * 25 = 75

And only one word has three A's

So...the total possible words = 1875 + 75 + 1 = 1951

CPhill Apr 22, 2018