Final answer:
To determine the number of possible committees with 2 women and 2 men from a group of 7 women and 7 men, calculate the combinations for each and multiply. There are C(7,2) ways to choose women and the same for men, resulting in 441 possible committees.
Step-by-step explanation:
To determine the number of possible committees with 2 women and 2 men from a group of 7 women and 7 men, calculate the combinations for each and multiply. There are C(7,2) ways to choose women and the same for men, resulting in 441 possible committees.
To solve the problem of forming a committee of 4 people with the condition that it consists of 2 women and 2 men from a group of 7 women and 7 men, we use combinations. The number of ways to choose 2 women from 7 is given by the combination formula C(7,2), which is 7! / (2!(7-2)!). Similarly, the number of ways to choose 2 men out of 7 is also C(7,2). The total number of different committees that are possible is the product of these two combinations.
The calculation is as follows:
- Number of ways to choose 2 women: C(7,2) = 21
- Number of ways to choose 2 men: C(7,2) = 21
- Total different committees possible: 21 * 21 = 441
Therefore, there are 441 different possible committees consisting of 2 women and 2 men.