It is currently 18 Oct 2017, 23:11

### 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

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

# A three-letter code is formed using the letters A-L, such th

Author Message
TAGS:
Manager
Joined: 20 May 2014
Posts: 113
Followers: 4

Kudos [?]: 24 [0], given: 84

A three-letter code is formed using the letters A-L, such th [#permalink]  09 Oct 2017, 23:10
00:00

Difficulty:

5% (low)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
A three-letter code is formed using the letters A-L, such that no letter is used more than once. What is the probability that the code will have a string of three consecutive letters (e.g. A-B-C, F-E-D)?

(A) 1/55

(B) 1/66

(C) 2/17

(D) 1/110

(E) 2/55

Kudos for correct solution.
[Reveal] Spoiler: OA
Manager
Joined: 20 Apr 2016
Posts: 202
Followers: 1

Kudos [?]: 118 [1] , given: 52

Re: A three-letter code is formed using the letters A-L, such th [#permalink]  10 Oct 2017, 04:52
1
KUDOS
Bunuel wrote:
A three-letter code is formed using the letters A-L, such that no letter is used more than once. What is the probability that the code will have a string of three consecutive letters (e.g. A-B-C, F-E-D)?

(A) 1/55

(B) 1/66

(C) 2/17

(D) 1/110

(E) 2/55

Kudos for correct solution.

Now let us arrange three letter code in the form (A-B-C) using the letters from A to L

i.e we have = ABC, BCD, CDE, DEF, EFG, FGH, GHI, HIJ, IJK, JKL

i.e we have 10 options.

Similarly we can write the three letter code in the form (F-E-D) i.e in opposite direction and we still have 10 options.

Therefore we have a total of 20 options, which is the favourable outcomes

Now Total outcomes = 12 * 11 *10 (Letters from A to L is 12 and here order matters, so we cannot use combination )

thereforeProbability =\frac{No. of favorable outcomes}{Total no. of outcomes}

orProbability = \frac{20}{(12*11*10}) = \frac{20}{1320} = \frac{1}{66}
_________________

If you found this post useful, please let me know by pressing the Kudos Button

Re: A three-letter code is formed using the letters A-L, such th   [#permalink] 10 Oct 2017, 04:52
Display posts from previous: Sort by