Last visit was: 08 May 2026, 23:58 It is currently 08 May 2026, 23:58
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
   1   2 
555-605 (Medium)|   Combinations|         
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 08 May 2026
Posts: 110,204
Own Kudos:
813,742
Given Kudos: 106,125
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 110,204
Kudos: 813,742
A certain stock exchange designates each stock with a one-, two- or th 03 Oct 2021, 01:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ak2121
Bunuel
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?

A. 2951
B. 8125
C. 15600
D. 16302
E. 18278

1 letter codes = 26
2 letter codes = 26^2
3 letter codes = 26^3

Total = 26 + 26^2 + 26^3

The problem we are faced now is how to get the answer quickly. Note that the units digit of 26+26^2+26^3 would be (6+6+6=18) 8. Only one answer choice has 8 as unit digit: E (18,278). So I believe, even not calculating 26+26^2+26^3, that answer is E.
Hi, should'nt we subtract 26 from 26^2 and 26^3 because AA,BB, CC or BBB,CCC,DDD will be occuring twice in the case?
Show more

26^2 gives the number of two-letter codes (this number includes same-letter codes: AA, BB, ...)
26^3 gives the number of three-letter codes (this number includes same-letter codes: AAA, BBB, ...)

As you can see there is not overlap between codes given by 26^2 and 26^3.
User avatar
GMATmona07
User avatar
Joined: 23 Jun 2022
Last visit: 13 Sep 2023
Posts: 24
Own Kudos:
4
Given Kudos: 79
Posts: 24
Kudos: 4
A certain stock exchange designates each stock with a one-, two- or th 06 Feb 2023, 18:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Number of one letter code-26
Number of two letter code- 26^2
Number of three letter code- 26^3

Total-26+26^2+26^3=18278

So ans is E.
User avatar
gracygupta23
User avatar
Joined: 16 Jan 2025
Last visit: 19 Apr 2026
Posts: 1
Given Kudos: 81
Posts: 1
Kudos: 0
A certain stock exchange designates each stock with a one-, two- or th 31 Aug 2025, 08:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Shouldn't we divide the two-digit code by 2 factorial and similarly three digit code by 3 factorial to eliminate repetition of the same letters like AAA or BBB etc? Even though repetition is allowed, we can't possibly shift these letters to make a new code.
Bunuel
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?

A. 2951
B. 8125
C. 15600
D. 16302
E. 18278

1 letter codes = 26
2 letter codes = 26^2
3 letter codes = 26^3

Total = 26 + 26^2 + 26^3

The problem we are faced now is how to get the answer quickly. Note that the units digit of 26+26^2+26^3 would be (6+6+6=18) 8. Only one answer choice has 8 as unit digit: E (18,278). So I believe, even not calculating 26+26^2+26^3, that answer is E.
Show more
User avatar
Krunaal
User avatar
Tuck School Moderator
Joined: 15 Feb 2021
Last visit: 30 Apr 2026
Posts: 852
Own Kudos:
919
 [1]
Given Kudos: 251
Status:Under the Square and Compass
Location: India
Schools: Ross '26 (M$$$$) Stern '26 (A) McCombs '26 (A$)
GMAT Focus 1: 755 Q90 V90 DI82
GPA: 5.78
WE:Marketing (Consulting)
Products:
My Reviews
Schools: Ross '26 (M$$$$) Stern '26 (A) McCombs '26 (A$)
GMAT Focus 1: 755 Q90 V90 DI82
Posts: 852
Kudos: 919
 [1]
A certain stock exchange designates each stock with a one-, two- or th 31 Aug 2025, 08:41
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gracygupta23
Shouldn't we divide the two-digit code by 2 factorial and similarly three digit code by 3 factorial to eliminate repetition of the same letters like AAA or BBB etc? Even though repetition is allowed, we can't possibly shift these letters to make a new code.

Show more
3 or 2 similar letters won't repeat; take a small example of 2 letters A and B => we get 2*2 = 4 different arrangements, viz. AA, AB, BA, BB. Similarly for 26 letters, you would get different no. of arrangements, you won't need to divide.
   1   2 
Moderators:
Bunuel
Math Expert
110204 posts
Krunaal
Tuck School Moderator
852 posts