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  4. A debate club consist of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 members) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is -

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Q. A debate club consist of $6$ girls and $4$ boys. A team of $4$ members is to be selected from this club including the selection of a captain (from among these $4$ members) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is -

JEE AdvancedJEE Advanced 2016

Solution:

Total No. of ways
$=\left({ }^{4} C _{0} \times{ }^{6} C _{4}+{ }^{4} C _{1} \times{ }^{6} C _{3}\right) \times{ }^{4} C _{1}$
$=(15+80) \times 4$
$=380$