Suppose that a department contains 10 men and 16 women. How many different committees of 6 members are possible if the committee must have strictly more women than men? Your answer is:

Step 1 ：Enumerate the possible committee member combinations based on gender:

Step 2 ：1) 1 man and 5 women: \(\binom{10}{1}\) ways to select men and \(\binom{16}{5}\) ways to select women. Total ways: \(\binom{10}{1}\binom{16}{5}\).

Step 3 ：2) 2 men and 4 women: \(\binom{10}{2}\) ways to select men and \(\binom{16}{4}\) ways to select women. Total ways: \(\binom{10}{2}\binom{16}{4}\).

Step 4 ：Calculate the sum of the above cases: \(\binom{10}{1}\binom{16}{5} + \binom{10}{2}\binom{16}{4}\)