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Question

110 children choose their favourite colour from blue and pink. Every student has to choose at least one of the colour. 60 children choose blue colour, while 70 children choose pink colour. How many children choose both the colours as their favourite colour?


Solution

Let A be the  number of students choosing blue and B be choosing pink
We have,
$$ n(A \cup B) = n(A) + n(B) - n(A \cap B ) $$
$$ 110 = 60 + 70 - n(A \cap B ) $$
$$ => n (A \cap B ) = 20 $$
So, $$20$$ students chose both the colours as their favourite colour.

Mathematics

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