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.