In a survey of 500 TV viewer, it was found that 285 watch cricket, 195 watch foodball and 115 watch tennis. Also, 45 watch both cricket and football, 70 watch both cricket and tennis, and 50 watch football and tennis, If 50 do not watch any game on TV. then the number of viewes watch all the games is

Explanation

Let `C` is the set of people who watch Cricket, `F` is the set of people who watch Football, `T` is the set of people who watch Tennis.

Then,

`n(CuuFuuT) = n(C)+n(F)+n(T)-n(CnnF)-n(FnnT)-n(CnnT)+n(CnnFnnT)`

As, `50` people do not watch any game,

So, total number of people who watch any of the games `= 500 - 50 = 450`

`:. n(CuuFuuT) = 450`

`:. 450 = 285+195+115-45-50-70+n(CnnFnnT)`

`=>n(CnnFnnT) = 450-430`

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