Answer:
Step-by-step explanation:
There are 15 antennas in total.
Out of these, 3 are defective.
This means that 12 antennas are functioning: 15-3=12.
To ensure that no two defective antennas are adjacent, we need to have only one defective at a time placed between the functional ones.
So,
We align the 13 functional antennas, then look for the spaces where the defective antennas can fit
__G __ G __ G __ G __ G __G __ G __ G __ G __ G __ G __ G __G __
Each gap represented by an underscore indicates a possible location for a defective antenna, allowing for just one per space.
Consequently, there are 14 potential spots for the defective antennas. With 3 defectives, we are dealing with a combinatorial arrangement.
ⁿCr= n!/(n-r)!r!
The total number of arrangements possible is
14C3=14!/(14-3)!3!
14C3=14×13×12×11!/11!×3×2
14C3=14×13×12/6
That gives us 364 distinct ways to arrange them.
