Answer: Option 'e' is correct.
Step-by-step explanation:
Since we have given that
Number of letters of the alphabet = 26
Number of letters in code :
One letter code, or two letter code, or three - letter code.
Since repetition of letters are allowed, then
if it is one letter code, the number of arrangement would be 26.
If it is two letter code, the number of arrangements would be
![26\times 26\\\\=26^2\\\\=676](https://tex.z-dn.net/?f=26%5Ctimes%2026%5C%5C%5C%5C%3D26%5E2%5C%5C%5C%5C%3D676)
If it is three letter code, the number of arrangements would be
![26\times 26\times 26\\\\=26^3\\\\=17576](https://tex.z-dn.net/?f=26%5Ctimes%2026%5Ctimes%2026%5C%5C%5C%5C%3D26%5E3%5C%5C%5C%5C%3D17576)
So, Number of different stocks to uniquely designate with these codes would be
![26+676+17576\\\\=18278](https://tex.z-dn.net/?f=26%2B676%2B17576%5C%5C%5C%5C%3D18278)
Hence, Option 'e' is correct.