probability

Question

I have 7 letters and 6 possibilities with repetition. so that is 7^6 but now they ask me how many word possibilities will not contain one of the letters, how many words will contain one of the letters at least once and then that same letter exactly twice.

Answer 1

So with words you won't be able to repeat the letters. 

For word possibilities that won't contain one letter assuming the word is 6 letters long that means you have 6 "spaces" to fill.  If you want to know how many words there are without using one of the letters, you take the letter away so now you only have 6 letters instead of 7 so it becomes 6*6*6*6*6*6. (you have 6 options to choose from for each space)

 

If you are saying the word has to have a certain letter, then that space becomes a 1 because there is only one option. But now you have taken that letter away from the seven choices so the rest of the spaces you will only have 6 letter to choose from. So words that contain one of the letters at least once becomes 1*6*6*6*6*6

If you want the same letter twice that means you have a 1 in two of the spaces. 1*1*6*6*6*6