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Find the number of ways that 9 people can be divided into 2 groups such that the first group has 5 people and the second group has 4 people.

User Jacky Lee
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3 votes

Answer:

126 ways

Explanation:

To find the number of ways to divide 9 people into two groups, with 5 people in the first group and 4 people in the second group, we can use the concept of combinations.

The number of ways to choose 5 people out of 9 to be in the first group is given by the combination formula:

C(9, 5) = 9! / (5! * (9 - 5)!) = 9! / (5! * 4!) = (9 * 8 * 7 * 6 * 5!) / (5! * 4 * 3 * 2 * 1) = (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1) = 9 * 2 * 7 = 126

This represents the number of ways to select 5 people from a group of 9 to be in the first group.

Once we have determined the first group, the remaining 4 people automatically form the second group.

Therefore, there are 126 different ways to divide 9 people into 2 groups such that the first group has 5 people and the second group has 4 people.

User Payam
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