Question 41948
We can see the pattern by looking at how many handshakes each person makes...
The first person can shake 21 hands, the second person can shake 20 hands, since they already shook hands with person #1, the 3rd person does 19, the 4th 18, and so on...
The sum of these 21 numbers is n(n+1) / 2 = 21(22) / 2 = 231.
In terms of the 22 people, it becomes (n-1)n / 2, and that is the general expression you need in part c...
Part b) Given there are 35 people, the number of shakes is 34(35) / = 17(35) = 595 handshakes...