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find the number of ways in which 9 people can be divided into 2 groups: the first group had 5 people and the second group has 4 people

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Final answer:

There are 126 ways to divide 9 people into two groups of 5 and 4, calculated using combinations formula.

Step-by-step explanation:

To find the number of ways in which 9 people can be divided into two groups where the first group has 5 people and the second group has 4 people, we use the concept of combinations. The formula for calculating combinations is nCr = n! / r!(n-r)!, where n is the total number of items, and r is the number of items to choose.

Since the arrangement within the groups doesn't matter, we only care about the selection of 5 people out of 9 for the first group.

The calculation is then as follows: 9C5 = 9! / (5!(9-5)!) = 9! / (5!4!) = (9×8×7×6) / (4×3×2×1) = 126 ways.

Therefore, there are 126 ways to divide 9 people into two groups of 5 and 4 people.

User Sadraque Santos
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