A group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected if the team has no girl?
A group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected if the team has no girl?
since, the team will not include any girl, therefore, only boys are to be selected. $5$ boys out of $7$ boys can be selected in $^{7} C _{5}$ ways.
Therefore, the required number of ways $=^{7} C _{5}=\frac{7 !}{5 ! 2 !}=\frac{6 \times 7}{2}=21$
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- [KVPY 2017]