Please help. Thank you

Fourteen people attend a meeting. If each person shook hands with every other person, how many handshakes were there altogether?

In combination notation, that would be

C(14,2) = 14!/(12!2!) or 91

Or

Each of the 14 people can shake hands with 13 other people, that would be 14x13 = 182 handshakes.
But that would be all cases of A shaking with B and B shaking with A, that is, we care counting each handshake twice.
So divide the 182 by 2 to get 91

To find the total number of handshakes, we can use a formula based on combinations.

In this scenario, we have 14 people, and each person needs to shake hands with every other person in the group.

To calculate the number of handshakes, we can use the combination formula: nC2 = n! / ((n - r)! * r!), where n represents the total number of people and r represents the number of people involved in each handshake (2 in this case).

So, plugging in the values, we get:

14C2 = 14! / ((14 - 2)! * 2!)

Calculating this expression, we get:

14! = 14 * 13 * 12 * ... * 2 * 1 = 87,178,291,200
(14 - 2)! = 12! = 12 * 11 * ... * 2 * 1 = 479,001,600
2! = 2 * 1 = 2

Now, let's substitute these values back into the formula:

14C2 = 87,178,291,200 / (479,001,600 * 2)
= 87,178,291,200 / 958,003,200
= 91

Therefore, there would be a total of 91 handshakes among the 14 people attending the meeting.