Question

10 houses are simultaneously kept. A thief can rob from any 3 houses but the houses cannot be consecutive. How many ways can he totally do it

Answer 1

Ans is 56

we can select any 3 house in 10C3 =120 ways.

No. of ways of selecting 3 houses such that all 3 are consecutive is 8.

And, number of ways in which exactly 2 houses are consecutive is (7*2 + 6* 7) = 56.

So, the answer is 120 - 8 - 56 = 56.