In a group of 16 players there are 4 bowlers and 2 wicketkeepers.From them a team of 11 is to be formed such that

1)there are at least 3 bowlers and exactly 1 wicketkeeper.Number of such teams=?

2))there are at least 3 bowlers and atleast 1 wicketkeeper.Number of such teams=?

Hello student,
Please find the answer to your question below
Given
1)In a group of 16 players there are 4 bowlers and 2 wicketkeepers.From them a team of 11 is to be formed such thatthere are at least 3 bowlers and exactly 1 wicketkeeper.
Number of such teams=2 (3 bowlers,1 wicketkeeper),(4 bowlers,1 wicketkeeper)
4c₃*2c₁*10c₇+4c₄*2c₁*10c₆=1380 ways
2)In a group of 16 players there are 4 bowlers and 2 wicketkeepers.From them a team of 11 is to be formed such thatthere are at least 3 bowlers and atleast 1 wicketkeeper.
Number of such teams=4(3b,1wkt),(3 b,2wkt),(4b,1wkt),(4b,2wkt)
4c₃*2c₁*10c₇+4c₃*2c₂*10c₆+4c₄*2c₁*10c₆+4c₄*2c₂*10c₅=2472 ways
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