I have a set of n antenna's of which m are defective, leaving n-m in working conditions. The defective and non-defective antenna's are to be considered indistinguishable (order of them is not important). How many linear orderning are there in which no two consecutive antenna's are defective?
Can anyone please help me on this?
we can approach this problem , consider the $n-m$ working antennas placed in a long queue this will generate $n-m+1$ spaces between them , of these spaces we have to choose any $m$ spaces and place defective antennas in those locations ! thus ensuring that no two effective antennas are together
the answer is : $ \binom{n-m+1}{m} $