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?

A.
56
B.
73
C.
80
D.
120
E.
None of the above

Accepted Answer

A. Number of ways to choose $k$ non-adjacent items from $n$ items in a row is $\binom{n - k + 1}{k}$. Here $n = 10, k = 3 \implies \binom{10 - 3 + 1}{3} = \binom{8}{3} = 56$.

Combinatorics: Non-adjacent Houses

Explanation

Practise this under exam conditions