Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 05 May 2015, 07:09

### 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

# Events & Promotions

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

# If you have the letters LOCAL, how many words can you form

Author Message
TAGS:
Intern
Joined: 04 Feb 2004
Posts: 28
Location: USA
Followers: 0

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

If you have the letters LOCAL, how many words can you form [#permalink]  19 Jan 2005, 19:15
If you have the letters LOCAL, how many words can you form where there is at least one space between the Ls?
Director
Joined: 31 Aug 2004
Posts: 606
Followers: 3

Kudos [?]: 43 [0], given: 0

How many words : 5!/2! = 60

Number of words with the 2 Ls next to each other : 4*3! = 24

My answer : 60 - 24 = 36
GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4313
Followers: 27

Kudos [?]: 217 [0], given: 0

Same approach as twixt and also got 36
_________________

Best Regards,

Paul

Director
Joined: 21 Sep 2004
Posts: 615
Followers: 1

Kudos [?]: 7 [0], given: 0

twixt wrote:
How many words : 5!/2! = 60

Number of words with the 2 Ls next to each other : 4*3! = 24

My answer : 60 - 24 = 36

Last edited by vprabhala on 20 Jan 2005, 11:39, edited 1 time in total.
GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4313
Followers: 27

Kudos [?]: 217 [0], given: 0

vprabhala wrote:
twixt wrote:
How many words : 5!/2! = 60

Number of words with the 2 Ls next to each other : 4*3! = 24

My answer : 60 - 24 = 36

5! is the number of letters.. and 2! we use cauz for a minimum word we need atleast 2 words is that it?

No, it's because letter "L" repeats 2 times
_________________

Best Regards,

Paul

Director
Joined: 07 Jun 2004
Posts: 614
Location: PA
Followers: 3

Kudos [?]: 276 [0], given: 22

LOCAL

Case 1
3 Spaces L x x x L the 3 OCA can be arranged 3! = 6

Case 2

2 spaces L x x L x or x L x x L can 3C2 * 3C2 ways = 9

Case 3

1 Space will be 3 ways

total number of ways will be 6 * 9 * 3 = 162 ways

RC can u please post the OA
GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4313
Followers: 27

Kudos [?]: 217 [0], given: 0

rxs0005 wrote:
LOCAL

Case 1
3 Spaces L x x x L the 3 OCA can be arranged 3! = 6

Case 2

2 spaces L x x L x or x L x x L can 3C2 * 3C2 ways = 9

Case 3

1 Space will be 3 ways

total number of ways will be 6 * 9 * 3 = 162 ways

RC can u please post the OA

rxs, I see you approached this problem the long way with favorable outcome approach. I agree with case 1 but for cases 2 and 3, there is a mistake in your reasoning

case2
LxxLx
xLxxL
For each of the above 2, you have 3! ways of arranging 3 other letters. So you have 3!*2 = 12

case3
LxLxx
xLxLx
xxLxL
Once again, for each of these possible ways of positioning "L", you have 3! ways of doing so. So it is 3!*3 = 18

So you have total favorable outcomes = case(1+2+3) = 6+12+18 = 36
_________________

Best Regards,

Paul

Director
Joined: 07 Jun 2004
Posts: 614
Location: PA
Followers: 3

Kudos [?]: 276 [0], given: 22

hey paul

thanks for the explantaion i mixed up counting with combinations

i get it now

rxs
Director
Joined: 07 Nov 2004
Posts: 694
Followers: 4

Kudos [?]: 29 [0], given: 0

rxs0005 wrote:
LOCAL

Case 1
3 Spaces L x x x L the 3 OCA can be arranged 3! = 6

Case 2

2 spaces L x x L x or x L x x L can 3C2 * 3C2 ways = 9

Case 3

1 Space will be 3 ways

total number of ways will be 6 * 9 * 3 = 162 ways

RC can u please post the OA

rxs, case 1 is good. But there is a problem in your case 2 and case 3.

For case 2:
For L _ _ L _ : You will have 3! ways, not 3C2
LOCLA;
LCOLA
LAOLC
LOALC
LACLO
LCALO

Similarly, for _ L _ _ L : You will have another 3! ways.

Case 3:
It should not be just 3 ways.
You will have:
L _ L _ _ : 3! ways for this arrangement
_ L _ L _ : 3! ways for this arrangement
_ _ L _ L : 3! ways for this arrangement

In the end you need to add all the ways not multiply.
So you get 6(3!) = 6*6 = 36
Director
Joined: 07 Nov 2004
Posts: 694
Followers: 4

Kudos [?]: 29 [0], given: 0

Similar topics Replies Last post
Similar
Topics:
7 How many words can be formed using all the letters of "EQUAT 8 16 Jun 2012, 19:38
11 How many words can be formed by taking 4 letters at a time 14 14 Apr 2010, 04:33
2 How many words can be formed from the letters of the word 7 19 Sep 2008, 01:19
10 How many different four-letter words can be formed (the words don't 13 12 Dec 2007, 11:15
How many words can be formed by taking 4 letters at a time 3 13 Jun 2005, 07:42
Display posts from previous: Sort by