Question

In how many ways can a committee of five democrats and six republicans be formed from a group of seven democrats and seven republicans?

Answer 1

There are 147 ways to form a committee with 5 Democrats and 6 Republicans.

Step-by-step explanation:

To find the number of ways a committee can be formed with five Democrats and six Republicans out of a group of seven Democrats and seven Republicans, we can use the concept of combinations. We need to select five Democrats out of seven and six Republicans out of seven. The number of ways to select k items from a set of n items is given by the formula nCk = n! / (k!(n-k)!).

So, the number of ways to select five Democrats from seven is 7C5 = 7! / (5!(7-5)!), and the number of ways to select six Republicans from seven is 7C6 = 7! / (6!(7-6)!).

Using factorial notation, we can simplify the calculations:

7C5 = 7! / (5!2!) = (7x6x5!) / (5!2!) = (7x6) / 2 = 21

7C6 = 7! / (6!1!) = (7x6!) / (6!1!) = 7

Now, we multiply the number of ways to select Democrats by the number of ways to select Republicans: 21 x 7 = 147.

Therefore, there are 147 ways to form the committee with five Democrats and six Republicans.