It is currently 10 Dec 2017, 21:17

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# permutations :S

 post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
Intern
Joined: 08 Jun 2009
Posts: 33

Kudos [?]: 44 [0], given: 0

permutations :S [#permalink]

### Show Tags

16 Jun 2009, 08:27
00:00

Difficulty:

(N/A)

Question Stats:

33% (01:46) correct 67% (00:00) wrong based on 12 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A certain stock exchange designates each stock with one-, two-, or three-letter code, where each letter is selected from the 26 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) 2,951
(B) 8,125
(C) 15,600
(D) 16,302
(E) 18,278

Kudos [?]: 44 [0], given: 0

Current Student
Joined: 13 May 2008
Posts: 141

Kudos [?]: 25 [0], given: 6

Schools: LBS
Re: permutations :S [#permalink]

### Show Tags

16 Jun 2009, 09:10
Jozu wrote:
A certain stock exchange designates each stock with one-, two-, or three-letter code, where each letter is selected from the 26 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) 2,951
(B) 8,125
(C) 15,600
(D) 16,302
(E) 18,278

stock with one-- 26
two-, 26*25= 650
or three-letter code, 26*25*24= 15,600

the total is 16,276 ... your option (d) is 16,302 thats intriguingly 26 more than my answer ... now i am probably doing something wrong but i can't figure it out and if you do, do post here b/c i am sort of curious now.

Kudos [?]: 25 [0], given: 6

Current Student
Joined: 03 Aug 2006
Posts: 115

Kudos [?]: 314 [0], given: 3

Location: Next to Google
Schools: Haas School of Business
Re: permutations :S [#permalink]

### Show Tags

16 Jun 2009, 09:18
Given that each letter in each stock code can be repeated we need to factor that in our calculations:

$$\text {No of 1 letter codes} = 26$$

$$\text {No of 2 letter codes} = 26\times 26 = 26^2$$

$$\text {No of 3 letter codes} = 26\times 26\times 26 = 26^3$$

$$\text {Total number of codes} = 26 + 26^2 + 26^3 = 18,278$$

The answer is E.

For the last step there is a faster way to get the answer than doing all the multiplication.

26 has 6 in the units digit.
Also 26^2 should have 6 in the units digit.
Similarly 26^3 should have 6 in the units digit.

If you add the units digits of the three it is 18 that would mean 8 would be in the units digit of the final answer and there is only one answer choice with 8 in the units digit i.e. E

See the following thread for more on last digit of a power.

last-digit-of-a-power-70624.html#p521012

Kudos [?]: 314 [0], given: 3

Intern
Joined: 08 Jun 2009
Posts: 33

Kudos [?]: 44 [0], given: 0

Re: permutations :S [#permalink]

### Show Tags

16 Jun 2009, 18:03
OA is E.

I'm a little confused here regarding permutations.

How do we know when to use nPr (order is relevant), nCr (order is not relevant) and your method above? I just can't seem to apply them correctly when I encounter such problems.

Kudos [?]: 44 [0], given: 0

Current Student
Joined: 03 Aug 2006
Posts: 115

Kudos [?]: 314 [0], given: 3

Location: Next to Google
Schools: Haas School of Business
Re: permutations :S [#permalink]

### Show Tags

16 Jun 2009, 20:33
This problem is testing the fundamental counting principal.

Here is a link to understand it better with some examples.

http://www.wtamu.edu/academic/anns/mps/ ... _count.htm

Also checkout this thread for more on Permutations and Combinations.

permutations-combinations-help-is-on-the-way-10838.html

Kudos [?]: 314 [0], given: 3

Founder
Joined: 04 Dec 2002
Posts: 15958

Kudos [?]: 29333 [0], given: 5290

Location: United States (WA)
GMAT 1: 750 Q49 V42
Re: permutations :S [#permalink]

### Show Tags

17 Jun 2009, 00:28
And of course the Walker's thread that is stickied in this forum: combinations-permutations-and-probability-references-56486.html
_________________

Founder of GMAT Club

Just starting out with GMAT? Start here... or use our Daily Study Plan

Co-author of the GMAT Club tests

Kudos [?]: 29333 [0], given: 5290

Re: permutations :S   [#permalink] 17 Jun 2009, 00:28
Display posts from previous: Sort by

# permutations :S

 post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.