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The number of ways in which a cricket team of 11 players be chosen out of a batch of 16 players so that the wicket-keeper of the team is always included, is

The number of ways in which a cricket team of 11 players be chosen out of a batch of 16 players so that the wicket-keeper of the team is always included, is Correct Answer <span style="position: relative; font-size: 10.5px; line-height: 0; vertical-align: baseline; top: -0.5em;">15</span>C<span style="position: relative; font-size: 10.5px; line-height: 0; vertical-align: baseline; bottom: -0.25em;">10</span>

Concept:

The number of ways of selecting r objects from n different objects subject to a certain condition like:

  • k particular objects are always included =  n - kCr - k
  • k particular objects are never included =  n - kCr

 

Calculation:

We know that, The number of ways of selecting r objects from n different objects subject to certain condition like:

  • k particular objects are always included =  n - kCr - k

∴ Total number of selection of 11 players out of 16 players in which wicket-keeper is included = 15C10 

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