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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