MATH SOLVE

4 months ago

Q:
# 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? a. 2,951 b. 8,125 c. 15,600 d. 16,302 e. 18,278

Accepted Solution

A:

Answer:There are 16276 different stocks which are possible to uniquely designate with these codesStep-by-step explanation:The information we have is that1. 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: [tex]P_{26|1} + P_{26|2}+ P_{26|3} \\26+650+15600= 16276[/tex]