List of practice Questions

Let \( S \) be the set of all ternary strings defined over the alphabet \( \{a, b, c\} \). Consider all strings in \( S \) that contain at least one occurrence of two consecutive symbols, that is, "aa", "bb", or "cc". The number of such strings of length 5 that are possible is ___________.

Let \( S \) be the set of all ternary strings defined over the alphabet \( \{a, b, c\} \). Consider all strings in \( S \) that contain at least one occurrence of two consecutive symbols, that is, "aa", "bb", or "cc". The number of such strings of length 5 that are possible is _________.

The number of arrangements of six identical balls in three identical bins is

There are 6 jobs with distinct difficulty levels and 3 computers with distinct processing speeds. The fastest computer gets the toughest job and the slowest computer gets the easiest job. Every computer gets at least one job. The number of ways in which this can be done is \(\underline{\hspace{2cm}}\).

If x is 1, 2, or 3 and y is either 2 or 4, then the product xy can have how many different possible values?