deltasquare,
there is no need of listing for 6 balls problem....
we need to select 6 balls from 7,8,5 balls
if i select 1 from 7, we are left with 6 ways of selecting remaining 5 balls from other 8,5 balls
similarly if 2 from 7, then 5 ways to select from 8,5 balls
...
...
if 6 from 7, then no need to select from 8,5 balls
so ans should be: 6+5+4+3+2+1 = 21
please lemme know any error as m very weak in P&C