Find the sum of cardinal numbers of the subsets

In mathematics, the cardinality of a set is a measure of the "number of elements" of the set. For example, the set A={2,4,6} contains 3 elements, and therefore A has a cardinality of 3

Question) A set has ‘n’ elements. Find the sum of the cardinal numbers of all the subsets of it.

Subscribe: BRAIN EXPLODERS

Watch the video and Learn Something Extraordinary...
00:00 | Question which was asked in the previous video
00:17 | Solution
03:17 | New Problem

Get early access and support the channel on Patreon

A challenge for you in the last of this video, can you solve that question? Take your time & give your answer in the comment section, if your answer is correct, we'll announce your name in our next YouTube video of this playlist - Exploders Contest: Season 2.

Previous Video
Title: Rumour in the Zoo - Find the Elephant Who Lost its Mass

Next Video
Title: Binary Numbers with Real Life Application - Find the working switch

Exploders Contest: Season 2

Exploders Contest: Season 1

This is the channel to feature this type of questions suggested by the people.

Support us on another platforms:
Patreon: BrainExploders
Instagram: Brain_Exploders
Facebook: BrainExploders
Twitter: BrainExploders
Telegram: Brain_Exploders

___Show your support to us.

________THANKS FOR WATCHING
#Brain_Exploders

_______________Next video will come soon

Brain Exploders geometry,
Brain Exploders ramanujan,
Brain Exploders math problem,
Brain Exploders iit jee,
Brain Exploders square,
Brain Exploders algebra,
Brain Exploders triangle,
Brain Exploders circle,
Brain Exploders area,
Brain Exploders amazon,
Brain Exploders area problem,
Brain Exploders area of triangle,
Brain Exploders area of square,
Brain Exploders a+b+c+d,
Brain Exploders angle,
Brain Exploders bodmas,
Brain Exploders books,
Brain Exploders balloon,
Brain Exploders birthday,
Brain Exploders books pdf,
Brain Exploders cube root,
Brain Exploders calculus,
mind your decision channel,
Brain Exploders circle square,
Brain Exploders division

[tomasdiaz]

For the new problem
The minimum number required is ONE.
The way to determine which switch is the one that works is to use binary numbers with the bulbs. There are 8 switches and 8 different possibilities on the bulbs.
We label the switches 1 through 8 and the light bulbs 3, 2, 1 where light bulb 3 is the hundreds position of the binary conversion; light bulb 2 is the tens position on the binary conversion and light bulb 1 is the ones.
So we connect one side of all the switches to the source. and the other side of each switch as follows:
Switch 1 connects to bulb 1 and nothing more
Switch 2 connects to bulb 2 and nothing more
Switch 3 connects to bulbs 1 and 2
Switch 4 connects to bulb 3 and nothing more
Switch 5 connects to bulbs 3 and 1
Switch 6 connects to bulbs 3 and 2
Switch 7 connects to all bulbs
Switch 8 connects to NOTHING
---
After all the connections are done you switch ALL of the switches to the ON position.
__
If Switch 1 is the one that works then the light bulbs will read 001
If Switch 2 is the one that works then the light bulbs will read 010
If Switch 3 is the one that works then the light bulbs will read 011
If Switch 4 is the one that works then the light bulbs will read 100
If Switch 5 is the one that works then the light bulbs will read 101
If Switch 6 is the one that works then the light bulbs will read 110
If Switch 7 is the one that works then the light bulbs will read 111
If Switch 8 is the one that works then the light bulbs will read 000
---
So once is connected this way all you have to do is enter the room ONCE and convert the on and off from binary to decimal. The decimal value will give you the only switch that works.

[tomasdiaz]

Answer to the new problem is ONLY ONE time to enter the room. I will be doing a better explanation of this soon.