Linda's teacher divided the class into groups of five and required each member of a group to meet with every other member of that group. How many meetings will each group have?

I know the answer is 10, but the problem is I can't find out the formula :/ if I only show the answer I won't get any credit and it'll be marked wrong.

5 per group.

person x = 1st person meeting everyone
x - 1, x - 2, x - 3, x-4 (no x - 5 because he/she is 5th person).
Meeting count:4

second person meeting everyone = y
y - 1, y -2, y - 3,
(no y -4 or y - 5 because he/she already met with person x and cannot meet with himself)
Meeting count: 7

third person meeting everyone = z
z - 1, z - 2
z has already met with y, z has already met with x, z cannot meet him/herself.
Meeting count: 9

fourth person meeting everyone = k
k -1
k has already met with x,y, and z. k cannot meet with himself

Meeting count:10
everyone has met with each other

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To find how many meetings each group will have, we need to determine the number of pairs combination that can be formed within a group of five.

In a group of five, each member needs to meet with every other member. This can be thought of as choosing 2 members at a time from a group of 5. The formula to calculate the number of combinations is nC2, where n represents the total number of people and 2 represents the number of people chosen at a time.

Using the combination formula, nC2 = n! / (2! * (n-2)!), where "!" denotes the factorial of a number.

For the given scenario, n = 5, so we can plug the values into the formula:

5C2 = 5! / (2! * (5-2)!)
= (5 * 4 * 3 * 2 * 1) / (2 * 1 * (3 * 2 * 1))
= (5 * 4) / 2
= 10

Hence, each group will have 10 meetings.