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. $m=n=78$
• B. $n=m-8$
• C. $m+n=68$
• D. $m=n=68$

Answer 1

Answer: (A)

$m=n=78$

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