1

Consider strings of length n taken from the restricted alphabet {a, b, c}. (a) How many such strings are there? (b) How many such strings are there with exactly two as? (c) How many such strings are there with at least two as? (d) How many such strings are there with exactly two as and at least one of each of the other letters?

i don't get what the question mean by "exactly two as" and " with at least two as"

  • Exactly 2 as means that there are only 2 a's in the entire string. At least 2 a's means that it could have 2 a's, or 3 a's, or 4 a's,....all the way to n a's. – Sherlock Holmes Oct 22 '14 at 05:37

1 Answers1

1

"Exactly two $a$s" means the letter $a$ occurs $2$ times and no more. If, for example, $n=6$, the possibilities include $$aabbcc\ ,\quad bababb\ ,\quad abcbba$$ but not $$abcbbc\ ,\quad baacca\ ,\quad aaaaaa\ .$$ "At least two $a$s" means $2$ and maybe more, for example, all of the above except $abcbbc$.

David
  • 82,662