wvspidermonkey
03-29-2008, 12:35 PM
A certain stock exchange designates each stock with a one, two, or three letter code where each letter is selected from 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?
2,951 8,125 15,600 16,302 18,278
My Answer:
26*26*26 = 17576. Each letter is selected from the 26 available for the three places. This does not consider the number of duplicates (aaa, bbb,ccc).
Formal Answer:
We need to count one, two, and three-letter codes: 26 + 26*26 + 26*26*26. Note that the unites digit of the sum will be 8, an observation that can save calculating time, but only if you are short on time! Answer is 18,278.
My question is… why 26 + 26*26 = 26*26*26 ?
2,951 8,125 15,600 16,302 18,278
My Answer:
26*26*26 = 17576. Each letter is selected from the 26 available for the three places. This does not consider the number of duplicates (aaa, bbb,ccc).
Formal Answer:
We need to count one, two, and three-letter codes: 26 + 26*26 + 26*26*26. Note that the unites digit of the sum will be 8, an observation that can save calculating time, but only if you are short on time! Answer is 18,278.
My question is… why 26 + 26*26 = 26*26*26 ?