Team Size =11 players

Case 1: 4 batsmen and 5 bowlers and 2 wicket-keepers

⇒ ^{6}C_{4 }× ^{7}C_{5} × ^{2}C_{2}

= (6×5/2) × (7×6/2) × 1

= 315

Case 2: 4 batsmen and 6 bowlers and 1 wickets keeper

⇒ ^{6}C_{4 }× ^{7}C_{6} × ^{2}C_{1}

= (6×5/2) ×7×2

= 210

Case 3: 5 batsmen and 5 bowlers and 1 wickets keeper

⇒ ^{6}C_{5 }× ^{7}C_{5} × ^{2}C_{1}

= 6×(7×6/2) ×2

= 252

So total number of ways = 315 + 210 + 252

= 777