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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=?

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=?
 

Grade:11

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
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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