Question

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

(A)10²(B)1023(C)2610(D)10!

Answer 1

Given :

Total number of lamps =10

Since at least one lamp is to be kept switched on

The total number of ways are

10C1+10C2+....10C10

⇒2¹⁰−1

⇒1024−1

⇒1023

Hence (B) is the correct answer.