Question

There are $10$ lamps in a hall. Each one of them can be switched on independently. The number of ways in which the hall can be illuminated is

• A. ${10}^2$
• B. $18$
• C. $2^{10}$
• D. $1023$

Answer 1

Answer: (D)

$1023$

Each bulb has two choices, either switched on or off

$\therefore$ Required number of ways

${=2}^{10}-1=1024-1=1023$

$[$ since in one way when all are switched off, the hall will not be illuminated].