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# Principle of Inclusion and Exclusion

Count to 100. How many of those numbers are odd or multiples of 5? Since 50 are odd and 20 are multiples of 5, at first glance the answer is 70...

How many students failed both subjects?

Find the sum of all natural numbers from 1 through 1000 which are neither divisible by 5 nor by 2.

\(175\) people can speak German,

\(150\) people can speak French,

\(180\) people can speak English,

\(160\) people can speak Japanese.

What is the minimum number of foreigners that can speak all the four languages?

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