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Question

A committee of $$11$$ members is to be formed from $$5$$ females. If m is the number of ways the committee is formed with at least $$6$$ males ad n is the number of ways the committee is formed with at least $$3$$ females, then?


A
m=n=78
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B
n=m8
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C
m+n=68
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D
m=n=68
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Solution

The correct option is C $$m=n=78$$
Since there are $$8$$ males and $$5$$ females. Out of these $$13$$, if we select $$11$$ persons, then there will be at least $$6$$ males and atleast $$3$$ females in the selection.
$$m=n=\left(\begin{matrix} 13 \\ 11\end{matrix}\right)$$ $$=\left(\begin{matrix} 13 \\ 2\end{matrix}\right)=\dfrac{13\times12}{2}=78$$.

Mathematics

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