Question

All stocks traded in U.S. stock markets are identified by a "ticker symbol" — an abbreviation of one to four letters. For example, Ford is "F," DuPont is "DD," Microsoft is "MSFT," and Harley-Davidson is "HOG." How many different stock ticker symbols are possible?

The answer is 475,254, but I don`t understand how this number was gotten

Answer 1

456,754

Explanation:

A ticker symbol is an abbreviation of one to four letters, which means it can be one letter, two letters, three letters or four letters. Each letter can be any of the 26 letters in the English alphabet, so there are 26 choices for each position.

For one letter ticker symbols:

26 (number of choices for the first letter) * 1 (number of positions) = 26 different possibilities.

For two letter ticker symbols:

26 (number of choices for the first letter) * 26 (number of choices for the second letter) = 676 different possibilities.

For three letter ticker symbols:

26 (number of choices for the first letter) * 26 (number of choices for the second letter) * 26 (number of choices for the third letter) = 17,576 different possibilities.

For four letter ticker symbols:

26 (number of choices for the first letter) * 26 (number of choices for the second letter) * 26 (number of choices for the third letter) * 26 (number of choices for the fourth letter) = 456976 different possibilities.

So, the total number of different stock ticker symbols that are possible is 26 + 676 + 17,576 + 456976 = 456,754.