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A TEAM OF 11 IS TO BE SELECTED OUT OF 14 PLAYERS  OF WHOM 5 AR BOWLRS.FIND THE NUMBER OF WAYS IN WHICH THIS CAN BE DONE SO AS TO INCLUDE AT LEAST 4 BOWLERS.

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  • This hypergeometric structure can be used when
    • NO order of selection.
    • No replacement of selection.

Both these conditions are valid in this problem:

  • Selction of players is unordered.
  • No replacement of players after selction is obvious. 

Further If question ask for the probability of  of selecting of a team with given condition of minimum 4 bowlers 

Required probability = $\frac{264}{\binom{14}{11}} = \frac{264}{364}$

where $\binom{14}{11}$ is the selection of 11 players out of 14 without any constraint.

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