combination tricky question A sports team consists of $5$ bowlers (or pitchers), $9$ batsman and $2$ keepers (or back-stops). How many different teams of $11$ players can be chosen from the above squad if the team consists of $6$ batsmen (pitchers) and at least $1$ keeper (back-stop)? Well, the answer is $1680$, which i didn't get it. My solution: ${9\choose 6}{2\choose 1}+ {9\choose 6}{2\choose 2}=252$ Am I right? :D

No you have left out poor bowlers.

The team can be formed in 2 ways.

1. 6 batsman, 1 keeper, 4 bowlers in ${9 \choose 6}{ 2 \choose 1}{ 5 \choose 4} = 840$
2. 6 batsman, 2 keeper, 3 bowlers in ${9 \choose 6}{ 2 \choose 2}{ 5 \choose 3} = 840$



So total number of ways = $1680$