OpenStudy (anonymous):

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.

5 years ago
OpenStudy (anonymous):

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....

5 years ago
OpenStudy (anonymous):

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...

5 years ago
OpenStudy (anonymous):

the answer is 56

5 years ago
OpenStudy (anonymous):

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.

5 years ago
OpenStudy (anonymous):

But i dont have any clue about it

5 years ago
OpenStudy (anonymous):

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

5 years ago
OpenStudy (anonymous):

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.

5 years ago
OpenStudy (anonymous):

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

5 years ago
OpenStudy (anonymous):

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

5 years ago