Find the number of ways in which 9 people can be divided into 2 groups: the first group has 5 people and the second group has 4 people.
To find the number of ways to divide 9 people into two groups, we can use combinations.
First, we need to choose 5 people from the total of 9 to form the first group. This can be calculated using the formula for combinations: nCr = n! / (r!(n-r)!), where n is the total number of items, and r is the number of items to be chosen.
In this case, we have 9 people in total, and we want to choose 5 for the first group. So, the number of ways to choose 5 people from 9 is calculated as: 9C5 = 9! / (5!(9-5)!) = 126.
After selecting the first group of 5 people, the remaining 4 people will automatically form the second group.
Therefore, there are 126 ways in which 9 people can be divided into 2 groups with 5 people in the first group and 4 people in the second group.
To find the number of ways to divide 9 people into 2 groups, we can use the concept of combinations.
To form the first group with 5 people, we need to choose 5 people from the total of 9. The number of ways to choose 5 people out of 9 is written as "9 choose 5" or denoted as C(9, 5).
The formula to calculate C(n, r), which represents choosing r items from a set of n items, is:
C(n, r) = n! / (r! * (n-r)!)
Using this formula, we have:
C(9, 5) = 9! / (5! * (9-5)!)
= (9 * 8 * 7 * 6 * 5!) / (5! * 4 * 3 * 2 * 1)
= 9 * 8 * 7 * 6 / (4 * 3 * 2 * 1)
= 3024 / 24
= 126
So, there are 126 ways to divide 9 people into 2 groups, where the first group has 5 people and the second group has 4 people.