# Set Theory, Calendars, Clocks and Binomial Theorem

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## Sets and Unions

In a survey it was found that 10% people don’t use Facebook, Twitter or Whatsapp.8% uses all the three. There are 15% who usesFacebook and Twitter, 20% who use Twitter and Whatsapp and 20% who useFacebook and Whatsapp. Number of people that use only Facebook, only Twitter and only Whatsapp are equal. If the survey was conducted on 1000 people, answer the following:
1.) How many people use Whatsapp only?
a)20 b)9 c)15 d)90
2.) What is the ratio of number of people that uses Whatsapp only to the people using either Whats app or Facebook or both?
a)1/6 b)25/75 c)1/3 d)1/9

90, 1/9

## Detailed Solution

Let the no. of people that use only Facebook = only Twitter = only Whatsapp = x
Let’s construct of venn diagram:

From the figure we can see that x + x + x + 8 + 20 + 20 + 15 + 10 = 100
=) 3x = 100 – 73
=) x = $\frac{27}{3}$ = 9
1.) Thus the of no people who use Whatsapp only = 9% or 9 x 1000/100 = 90
2.) % of people that use Whatsapp only = 9
% of people that use either Whatsapp or Facebook or both = 20 + 20 + 8 + 9 + 9 +15 = 81 Thus the ratio = $\frac{9}{81} = \frac{1}{9}$

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