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  • 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__________.

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__________.
 

Answers (1)

best_answer

7 batsmen , 6 bowlers  and 2 wicketkeeper are available for selection.

Possible ways  to select the team :

  Batsmen Bowlers wicketkeepers
1. 6 4 1
2. 5 4 2
3. 5 5 1

So number of ways

\begin{aligned} &= ^{7} C_{6} \cdot{ }^{6} C_{4} \cdot{ }^{2} C_{1}+{ }^{7} C_{5}{ }^{6} C_{4} \cdot{ }^{2} C_{2}+{ }^{7} C_{5}{ }^{6} C_{5}{ }^{2} C_{1} \\ &=777 . \end{aligned}

Hence , the correct answer is 777.

Posted by

Kuldeep Maurya

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