My answer is C

here it goes..

for 4 letter code its 26^4
5 letter code its 26^5

the maximum ways is 26^4+26^5

26^4+ 26^4*26

26^4(26+1)

hence 27(26^4)

I know this may sound like a very basic concept to many of you but for me it is not very clear why we don't use the combinations formula 26 choose 4 to find out the possible combinations of making 4 digit stock codes out of the 26 letters of the alphabet.

I would really appreciate any assistance in explaining why we just calculate it as 26^4? Also, what would cause us to calculate it as 26 choose 4 using the combintaions formula instead?

Knowing these differences is key for me to get a solid grasp on combinations because I don't seem to have a logical grasp of combinations applications yet.

Thanks in advance

You should read up more on permutations and combinations and learn from examples. That was what I did, and still doing, cos I find myself weak in permutations too...

For e.g this website has some good examples:- https://www.questionbank.4gmat.com/mba_p ... obability/

For your qn, 4 digit code can be visualized like 4 spaces, i.e _ _ _ _, which can be filled up by any of 26 letters.

At the first space, you can choose any of the 26 letters, right? And next, you go to the 2nd space, you find that you can choose any of the 26 letters too. So on..

That would mean we have combinations of 26*26*26*26 = 26^4. The same logic can be applied to the 5 digits to get 26^5. The qn is kind enough to let us re-use the letters so we do not have to factor anything else.

And since it says either 4 digit or 5 digit, it means that we need to add up the numbers cos we can choose from ANY of the combinations, be it 4 or 5 digit.

Hope this helps you...Maybe the experts could give their valuable inputs!

Well the reason you do not use combinations is because we can use the alphabets again, that is to say that they are replaceable

If they question contained the clause that no alphabet is to be repeated, then combinations would do the trick.

Just keep in mind. If we can replace and reuse NO combinations

HTH

Thanks eaakbari