Explanation

(d)
The number of ways in which at least 5 women can be included in a committee
$= \ ^{9}C_{5} \times \ ^{8}C_{7} + \ ^{9}C_{6} \times \ ^{8}C_{6} + \ ^{9}C_{7} \times \ ^{8}C_{5} + \ ^{9}C_{8} \times \ ^{8}C_{4} + \ ^{9}C_{9} \times \ ^{8}C_{3}$
(i) Women are in majority, then number of ways
$= {\ ^{9}C}_{7} \times \ ^{8}C_{5} + \ ^{9}C_{8} \times \ ^{8}C_{4} + \ ^{9}C_{9} \times \ ^{8}C_{3}$
$= 2016 + 630 + 56 = 2702$
(ii) Men are in majority, then number of ways
$= \ ^{9}C_{5} \times \ ^{8}C_{7} = 126 \times 8 = 1008$