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(C) To select a committee of $30$ persons such that the number of boys,girls,and teachers is equal,we must select $10$ boys,$10$ girls,and $10$ teache

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$\frac{(20!)^3}{(10!)^6}$

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(C) To select a committee of $30$ persons such that the number of boys,girls,and teachers is equal,we must select $10$ boys,$10$ girls,and $10$ teachers.The number of ways to select $10$ boys from $20$ is $^{20}C_{10} = \frac{20!}{10!10!}$.The number of ways to select $10$ girls from $20$ is $^{20}C_{10} = \frac{20!}{10!10!}$.The number of ways to select $10$ teachers from $20$ is $^{20}C_{10} = \frac{20!}{10!10!}$.Since these selections are independent,the total number of ways is the product of these individual combinations:Total ways $= \frac{20!}{10!10!} 	imes \frac{20!}{10!10!} 	imes \frac{20!}{10!10!} = \frac{(20!)^3}{(10!)^6}$.

The number of ways of selecting a committee of $30$ persons from $20$ boys,$20$ girls,and $20$ teachers such that the participation of the number of boys,girls,and teachers in that committee is equal,is

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