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

Question

If you have the letters LOCAL, how many words can you form where there is at least one space between the Ls?

twixt · Answer

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

Paul · Answer

Same approach as twixt and also got 36

vprabhala · Answer

<img src="{SMILIES_PATH}/icon_rolleyes.gif" alt=":roll:" title="Rolling Eyes" />

Paul · Answer

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

rxs0005 · Answer

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

Paul · Answer

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

rxs0005 · Answer

hey paul 

thanks for the explantaion i mixed up counting with combinations 

i get it now

rxs

gayathri · Answer

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

gayathri · Answer

oops, did not realize Paul had already explained.

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

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