There are 6 bowlers and 9 batsmen in a cricket club. In how many ways can a team of 11 be selected so that the team contains at least 4 bowlers?

Possibilities     Bowlers      Batsmen         Number of ways

                         6               9

         1              4                7               $(6C4*9C7)$

         2              5                6               $6C5*9C6$

         3              6                5               $6C6*9C5$

$6C4*9C7$ = 15 x 36 = 540

$6C5*9C6$ = 6 x 84 = 504

  $6C6*9C5$= 1 x 126 = 126

Total = 1170