NCHMCT JEE 2021 Question Paper with solutions for online practice

Since, there are 9 women and 8 men. So, a committee of 12 consisting of atleast 5 women, can be formed by choosing.
(i) 5 women and 7 men
(ii) 6 women and 6 men
(iii) 7 women and 5 men
(iv) 8 women and 4 men
(v) 9 women and 3 men
$\therefore$ Total number of ways of forming the committee
$={}^9{\mathit{C}}_5\times {}^8{\mathit{C}}_7+{}^9{\mathit{C}}_6\times {}^8{\mathit{C}}_6+{}^9{\mathit{C}}_7\times {}^8{\mathit{C}}_5$
$+{}^9{\mathit{C}}_8\times {}^8{\mathit{C}}_4+{}^9{\mathit{C}}_9\times {}^8{\mathit{C}}_3$
$=1008+2352+2016+630+56=6062$