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?A. 2951B. 8125C. 15600D. 16302E. 18278

Answer 1

E. 18278

Explanation:

With one letter:

There are 26 letters. So with one letter, you can build 26 different codes.

With two letters:

For each letter of the code, there are 26 options. So there are 26*26 = 676 possible two-letter codes.

With three letters:

For each letter of the code, there are 26 options. So there are 26*26*26 = 17576 possible three letter codes.

Total:

26+676+17576 = 18278