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How many ways exist to form 3 groups from 14 people if each

group should contain at least 2 people?

User Pelagos
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4 votes

Answer:

To solve this problem, we can use the combination formula, which is:

nCr = n! / (r! * (n - r)!)

where n is the total number of items (people in this case) and r is the number of items we want to select (the group size in this case).

To form 3 groups from 14 people, we can start by selecting 2 people for each group, which gives us:

C(14, 2) ways to select 2 people for the first group

C(12, 2) ways to select 2 people for the second group (after 2 people are already chosen for the first group, there are 12 people left to choose from)

C(10, 2) ways to select 2 people for the third group (after 4 people are already chosen for the first two groups, there are 10 people left to choose from)

To find the total number of ways to form 3 groups, we can multiply the number of ways to select people for each group:

C(14, 2) * C(12, 2) * C(10, 2) = 91 * 66 * 45 = 272,970

Therefore, there are 272,970 ways to form 3 groups from 14 people if each group should contain at least 2 people.

User Matthew Simoneau
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8.7k points

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