Stock Exchange

[Atonio79]

A certain stock exchange designates each stock with one-, two-, three- letter code, where each letter is selected from the 25 letters of the alphabet. If the letters may be repeated and if the same letters used in different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes?

a. 2951
b. 8125
c. 15600
d. 16302
e. 18278

[Anson800]

Imo C

[GmatG]

This is wot I did...

1-letter codes will be 25
2-letter codes will be 25*25=625
3-letter codes will be 25*25*25= 625*25 =15625

So, Total no. of codes will be 16275 (1+2+3)

Please post the OA. Also Confirm the options once.

[NishantG]

Answer should be 16275

[ramiy]

Can anybody explain the solution ?
Gmat G why did u take 25*25 and for the third case 25*25*25 .

Dont we have to apply combinations formula

25 + 25C2 + 25C3 . Please correct me if iam wrong

[NishantG]

If the letters may be repeated and if the same letters used in different order constitute a different code-This statement means that this is a probability question and not combinations

[Atonio79]

The correct answer is E- 18,278

[Makumajon]

Hi Atonio, your answer is possible when you consider all the 26 letters of the alphabet. Approaches of GmatG & Nishant are right. So, if OA is E, then there must be typo in Q-step, i.e., 26 instead of 25.

In that case, 26+26*26+26*26*26=18,278

[Atonio79]

Sorry but there was a typo. It should have said 26 letters instead of 25. Thanks for the feed back!

[GmatG]

Originally Posted by Makumajon

Hi Atonio, your answer is possible when you consider all the 26 letters of the alphabet. Approaches of GmatG & Nishant are right. So, if OA is E, then there must be typo in Q-step, i.e., 26 instead of 25.

In that case, 26+26*26+26*26*26=18,278

Agree with Makumajon!