(a) To form a committee with more men than women, consider the following cases:

1. 5 men and 0 women: \(\binom{8}{5} \times \binom{7}{0} = 56\)
2. 4 men and 1 woman: \(\binom{8}{4} \times \binom{7}{1} = 490\)
3. 3 men and 2 women: \(\binom{8}{3} \times \binom{7}{2} = 1176\)

Adding these gives the total number of ways: \(56 + 490 + 1176 = 1722\).

(b) To divide the 15 members into groups of 3, 5, and 7:

First, choose 3 people for the first group: \(\binom{15}{3}\).

Then, choose 5 people for the second group from the remaining 12: \(\binom{12}{5}\).

The remaining 7 people form the last group: \(\binom{7}{7} = 1\).

The total number of ways is \(\binom{15}{3} \times \binom{12}{5} = 455 \times 792 = 360360\).