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In a group of 37 boys, 21 boys like football and 13 boys like both football and cricket. If every boy likes at least one of the two sports, how many boys like only cricket?

In a group of 37 boys, 21 boys like football and 13 boys like both football and cricket. If every boy likes at least one of the two sports, how many boys like only cricket? Correct Answer 16

Given:

Total boys = 37

Numbers of boys who like football = 21

Number of boys who like football and cricket = 13

Calculation:

Total number of boys, n(A∪B) = 37

Number of boys like both football and cricket, n(A∩B) = 13

Number of boys like football, n(A) = 21

Let, number of boys like only cricket, n(B) = x

According to set theory formula,

⇒ n(A∪B) = n(A) + n(B) – n(A∩B)

⇒ 37 = 21 + x – 13

⇒ x = 50 – 21

⇒ x = 29

Number of boys like cricket 29

⇒ Number of boys like only cricket = (29 - 13) = 16

∴ 16 boys like only cricket.

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