From a class of 15 boys and 12 girls, 9 students are to be chosen for the competition. In how many ways can the selection be made?

^{15} C_{9}

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12 C_{9}

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^{27} C_{9}

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All of the above.

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Solution

The correct option is C $^{27} C_{9}$
Given that their are $15$ boys and $12$ girls in a class.

That comprises of total $27$ students.

Also, as we know that number of ways of selecting "r" things out of "n" different things is equal to $^{n} C_{r} .$

So, number of ways of selecting $9$ students from total of $27$ students in clas can be done in $^{27} C_{9}$ ways.

$\Rightarrow^{27} C_{9} = \frac{27!}{(27 - 9)! .9!} = \frac{27!}{21! .9!}$

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