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Standard XII

Mathematics

Venn Diagram

In a team of ...

Question

In a team of 11, seven are batsmen, six are bowlers and one of them is a wicket keeper-batsman. How many of them are all-rounders (both batting and balling)?

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Solution

We should assume here that everyone is either a batsman or a bowler. The Venn diagram will look like

The wicket keeper batsman is inside the circle of batsmen. We know there are total of 11 players.

Total number of players = 1 wicket keeper + 6 batsmen + 6 bowlers - n all-rounders

11 = 1+ 6 + 6 - n = 13 - n

n = 2

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