Final answer:
There are 10,650 ways to form a committee of 6 people from a group of 10 men and 12 women, with the committee having more men than women. This is calculated using combinations for the distinct scenarios where men outnumber women.
Step-by-step explanation:
The question asks how many ways there are to select 6 people to form a committee from a group of 10 men and 12 women, where the committee must have more men than women. This is a combinatorial problem and can be solved using combinations. Since there must be more men than women, the potential committees could consist of 3 men and 2 women, 4 men and 1 woman, or all 6 men and no women. The number of ways to choose k men from a group of 10 is given by the combination formula C(10, k), where k can be 3, 4, or 6.
To calculate the total number of ways to form the committee, we can find the sum of the products of each combination of men and women. For example, when selecting 3 men and 2 women, the calculation is C(10, 3) * C(12, 2). Similarly, for 4 men and 1 woman, the calculation is C(10, 4) * C(12, 1), and for 6 men and no women, it's C(10, 6) * C(12, 0).
Combining these calculations:
- 3 men and 2 women: C(10, 3) * C(12, 2) = 120 * 66 = 7920
- 4 men and 1 woman: C(10, 4) * C(12, 1) = 210 * 12 = 2520
- 6 men and 0 women: C(10, 6) * C(12, 0) = 210 * 1 = 210
The total number of ways is the sum of all the products: 7920 + 2520 + 210 = 10650.