In a locality, there are ten houses in a row. On a particular night a thief planned to steal from three houses

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?

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Accepted Answer

56. Total number of houses = 10 If first house is robbed, then II is not and if II house is robbed, then III is not and so on. Thus 2 adjacent houses can never be chosen So, number of ways in which three houses can be robbed such that no two of them are next to each other. = C 3 10 − 2 = C 3 8 C^{10 - 2