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?
Correct answer: E
I got answer correct but took 3min30s to solve this question.
My approach was as following:
1 letter codes: 26 ways
2 letter codes: (2P26) + 26 = 676 ways
3 letter codes: (3P26) + 3*(1P26)*(1P25)+(1P26) = 17576 ways
Sum = 26+676+17576 = 18278
Please find my manuscript in the attached.
I found my way is too time consuming since we have to solve a single problem within a two-minite timeframe. There should be a better/simpler way to think, right?
Your detailed instruction will be highly appreciated!！