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# A committee of 11 members is to be formed from 8 males and 5 females.

Question:

A committee of 11 members is to be formed from 8 males and 5 females. If $\mathrm{m}$ is the number of ways the committee is formed with at least 6 males and $n$ is the number of ways the committee is formed with at least 3 females, then :

1. $\mathrm{m}=\mathrm{n}=78$

2. $\mathrm{n}=\mathrm{m}-8$

3. $m+n=68$

4. $\mathrm{m}=\mathrm{n}=68$

Correct Option: 1

Solution:

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.

$\mathrm{m}=\mathrm{n}=\left(\begin{array}{l}13 \\ 11\end{array}\right)=\left(\begin{array}{l}13 \\ 2\end{array}\right)=\frac{13 \times 12}{2}=78$