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

Answer 1

RD SHARMA... right..?.

Well answer is 1023 ways..
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

⇒2^10−1

⇒1024−1

⇒1023 ways...



Don't forget to mark itvas brainy..

Answer 2

Answer:

The number of ways in which the hall can be illuminated is 1023 .

Step-by-step explanation:

Explanation :

Given ,total number of lamps in a hall = 10

And each of them can be switched on independently .

This means that , an every bulbs 2 options either on .

Step 1:

So  , the total numbers of ways will be = $2^{10}$

We required at least one lamp is to be switched on to illuminate the hall .

Therefore , there will be only one way when the hall will not be illuminated.

So , the numbers of ways in which the hall can be illuminated

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

Final answer:

Hence , there are  1023 ways in which the hall can be illuminated.

#SPJ2