Because we can use all 26 letters in any way (including multiple times), and the order is important:

For 5 letter OTCs, there are 26^5 possibilities
For 4 letter OTCs, there are 26^4 possibilities

So our answer is:
26^5+26^4 = 26^4 *26 + 26^4 = 26^4 (26+1) = 27(26^4) ANS C.

How did you come up with 26^5 and 26^4? Can you break this problem down or can you give me the thought process behind your logic.

Thanks.

Also why is order important...

Sure...

All the stocks are identified by 4 or 5 letters.

So we could have the following:

AAAA
AAAAA
ABAAB
ABCDE
ABCD

All of which are different. Order is important because AABB is not the same as BBAA or ABAB.

Let's start with the 4 letter stocks:
We can have any one of 26 letters in the first position, and one of 26 letters in the second position, etc. For this type of combinations (where order is important ), we simply multiply the number of possibilities in each position: So: 26*26*26*26 = 26^4

Then we can do the same thing for the 5 letter stocks and get:
26*26*26*26*26 = 26^5.. From here we just need to simply as I did above.

Hope this helps.

Thanks for your explanation.....

no problem..

Here's a great resource on probability:

https://www.mansw.nsw.edu.au/members/ref ... no4yen.htm