Latest Elitmus Aptitude Question SOLUTION: In a locality there are ten houses in a row. On a particular night a thief planned to steal from three houses of locality. In how many ways can he plan such that no two houses are

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(#M40155568) ELITMUS Numerical Ability question Keep an EYE

In a locality there are ten houses in a row. On a particular night a thief planned to steal from three houses of locality. In how many ways can he plan such that no two houses are next to each other?
Options are:
56, 73, 80, 100

Asked In Elitmus Rizul (8 years ago)

Solved Sufal Ghosh Read Solution (3)

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Read Solution (3) :

sahil aggarwal  (8 years ago)

The answer would be 56.
Lets say we have removed the three said houses. Now we are left with 7 houses.
If we arrange these 7 houses we have 8 places to put the other 3 houses at.

_ H1 _ H2 _ H3 _ H4 _ H5 _ H6 _ H7 _

so 8C3 = 56

Is this solution Helpfull? Yes (93) | No (3)  

Sufal Ghosh  (8 years ago) Best Solution

I think ,it will be 56...
assume that the thief start from 1st house then 3rd house and then 5th house to any of remaining 5th houses..
1st step:the thief can stole from 1st house ,3rd and from 5 house; there are 6+5+4+3+2+1=21 ways
2nd step:the thief can stole from 2nd house,4th house and from 6th house ;there are 5+4+3+2+1=15 ways
3rd step:the thief can stole from 3rd ,5th and from 7th; there are 4+3+2+1=10 ways
4th step: the thief can stole from 4th , 6th and from 8th ;there are 3+2+1=6 ways
5th step:the thief can stole from 5th ,7th and from 9th ;there are 2+1=3 ways
6th step:the thief can stole from 6th , 8th and from 10th ;there is 1 way

So total(1+3+6+10+15+21)=56

Is this solution Helpfull? Yes (16) | No (10)  

sameer  (4 years ago)

The answer would be 56.
Lets say we have removed the three said houses. Now we are left with 7 houses.
If we arrange these 7 houses we have 8 places to put the other 3 houses at.

_ H1 _ H2 _ H3 _ H4 _ H5 _ H6 _ H7 _

so 8C3 = 56

Is this solution Helpfull? Yes | No (2)  

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