There are 10 teachers and 20 students out of which selection of $5$ students are made for a sports committee. Find the number of ways in which this selection can be done.

\frac{10!}{5! .5!}

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\frac{20!}{15! .5!}

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\frac{20!}{10! .5!}

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None of the above

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Solution

The correct option is B $\frac{20!}{15! .5!}$
There are $10$ teachers and $20$ students out of these $5$ students are selected for sports committee.

Here, selection of students is only done. No teachers are selected.

So, all the possible selection of $5$ students out of $20$ students are made and it is equal to $^{20} C_{5} .$

$\Rightarrow^{20} C_{5} = \frac{20!}{(20 - 5)! 5!} = \frac{20!}{15! .5!}$

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There are 10 teachers and 20 students out of which selection of 5 students are made for a sports committee. Find the number of ways in which this selection can be done.

There are 10 teachers and 20 students out of which selection of $5$ students are made for a sports committee. Find the number of ways in which this selection can be done.