There are $5$ lamps in a line. How many combinations are there with $2$ or more on? There is $1$ combination where all lamps are turned on and $5$ where any one of them is turned on.
There are $4$ combinations when $2$ or more lamps are on. $2$ on $3$ off, $3$ on $2$ off, $4$ on $1$ off, $5$ on $0$ off. But what will be the correct answer according to the question?
There are $2$ possibilities for a lamp: ON or OFF. For $5$ lamps there are $2^5=32$ combinations.
The remaining combinations have $2$ ore more lamps turned on. The number of remaining combinations is therefore $32-5-1=26.$