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:
Correct Option: , 2
Since, $m=$ number of ways the committee is formed with at least 6 males
$={ }^{8} \mathrm{C}_{6} \cdot{ }^{5} \mathrm{C}_{5}+{ }^{8} \mathrm{C}_{7} \cdot{ }^{5} \mathrm{C}_{4}+{ }^{8} \mathrm{C}_{8} \cdot{ }^{5} \mathrm{C}_{3}=78$
and $n=$ number of ways the committee is formed with at least 3 females
$={ }^{5} \mathrm{C}_{3} \cdot{ }^{8} \mathrm{C}_{8}+{ }^{5} \mathrm{C}_{4} \cdot{ }^{8} \mathrm{C}_{7}+{ }^{5} \mathrm{C}_{5} \cdot{ }^{8} \mathrm{C}_{6}=78$
Hence $m=n=78$
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