There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is

Step-by-step solution

We have, 15   : Players 6   : Bowlers 7   : Batsman 2   : Wicket keepers Total number of ways for at least 4 bowlers, 5 batsman and 1 wicket keeper = C 4 6 × C 6 7 × C 1 2 + C 4 6 × C 5 7 × C 2 2 + C 5 6 × C 5 7 × C 1 2 = 777