[Question PS-Prep]

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?

A2,951

B8,125

C15,600

D16,302

E18,278

Correct answer: E

[My question]

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!！

Best regards,

Fuhe(Helia) Jin