JEE MAIN - Mathematics (2021 - 20th July Morning Shift - No. 22)
There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsman 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 batsman and 1 wicketkeeper, is ______________.
Answer
777
Explanation
15 : Players
6 : Bowlers
7 : Batsman
2 : Wicket keepers
Total number of ways for :
at least 4 bowler, 5 batsman & 1 wicket keeper
= $${}^6{C_4}({}^7{C_6} \times {}^2{C_1} + {}^7{C_5} \times {}^2{C_2}) + {}^6{C_5} \times {}^7{C_5} \times {}^2{C_1}$$
$$ = 777$$
6 : Bowlers
7 : Batsman
2 : Wicket keepers
Total number of ways for :
at least 4 bowler, 5 batsman & 1 wicket keeper
= $${}^6{C_4}({}^7{C_6} \times {}^2{C_1} + {}^7{C_5} \times {}^2{C_2}) + {}^6{C_5} \times {}^7{C_5} \times {}^2{C_1}$$
$$ = 777$$
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