Question

A certain stock exchange designates each stock with a one-, two-, or three-letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes?

Answer 1

Answer:

There are 16276 different stocks which are possible to uniquely designate with these codes

Step-by-step explanation:

The information we have is that

1. There are 26 different letters.

2. The stock can be designated with a one, two or three letter code and the letters may be repeated (We always have 26 options for the first, second and third letter)

3. Order matters (different order constitute a different code), which means we're talking about permutations.

The total codes we can make would be:

$P_{26|1} + P_{26|2}+ P_{26|3} \\26+650+15600= 16276$