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)?
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