Question

In a locality there are ten houses in a row.On a particular night a thief planned to steal from three houses of the locality.In how many ways can he plan such that no two of them are next to each other.

Kindly post the answer with proper justification/explanation.

Answer 1

I think you can just take cases and add them up....
suppose he robs first house, he can rob the rest in6+5+4+3+2+1 ways
If he robs second house, he cn rob the rest in 5+4+3+2+1 ways and so on....

Answer 2

err if you want explanation why 6+5+4+3+2+1 then its bcoz if you take first house then you can select from 3rd house onward, if you take 3rd house you can select from 5-10 =6 . now if second house is fourth you get 5 and so on...

Answer 3

the answer is 56

Answer 4

56 different ways I think. If you call the houses as such: 0 1 2 3 4 5 6 7 8 9 then he could break into 0 2 4, 0 2 5, 0 2 6 etc. This is a combination of 3 out of 8. Calculate this as 8C3:
\[\Large \begin{array}{l}
nCk = \frac{{n!}}{{k!(n - k)!}}\\
\frac{{8!}}{{3!(8 - 3)!}} = \frac{{40320}}{{720}} = 56
\end{array}\]
Alternatively, you can write out every single possible combination - from 0 2 4 to 5 7 9 I think it should be - and I'm quite confident you'd still find 56.

Answer 5

But i dont have any clue about it

Answer 6

why u choosed out of 8???can you please explain it...

Answer 7

Because of how the houses are arranged and how he can break into them.
Here's a much better explanation, courtesy of a bit of Googling (which OpenStudy users should learn to do;)) -> http://www.gyancentral.com/articles/post-graduate/mba/mba-entrance-exams/cracking-xat-2012:-shaping-up-your-quantitative-ability-skills?print=1&tmpl=component
See Part B.

Answer 8

That i did it already but I am not getting the logic behind it... :(

Answer 9

he steals from 3 houses and leaves 7 houses.
we represent these 7 houses by Ns and Y for 3 houses and then arrange them in a straight line- YNYNYNYNYNYNYNY
Thus.We get 8 vacant places denoting the houses from where the thief can steal
Now we have to just select 3 out of 8 vacant places which is 8C3 =56 ways