A committee of 11 members is to be formed from 8 males and 5 females. If \(m\) 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

A committee of 11 members is to be formed form 8 males and 5 females.
\(\therefore\) When atleast 6 males are included, the committee contains
(6 Males and 5 females), (7 males and 4 females), (8 males and 3 Females)
\(\therefore\) Required number of ways
\( ={ }^8 \mathrm{C}_6 \times{ }^5 \mathrm{C}_5+{ }^8 \mathrm{C}_7 \times{ }^5 \mathrm{C}_4+{ }^8 \mathrm{C}_8 \times{ }^5 \mathrm{C}_3 \)
\( \therefore \mathrm{m}=78 \)
When atleast 3 females are included, the committee contains (3 females and 8 males), (4 females and 7 males), (5 females and 6 males)
\( \therefore\) Required number of ways
\( ={ }^5 \mathrm{C}_3 \times{ }^8 \mathrm{C}_8+{ }^5 \mathrm{C}_4 \times{ }^8 \mathrm{C}_7+{ }^5 \mathrm{C}_5 \times{ }^8 \mathrm{C}_6 \)
\( =78 \)
\( \therefore \mathrm{n}=78 \)
\( \therefore \mathrm{m}=\mathrm{n}=78\)