Question

seven people meet and shake hands with eachother- how many handshakes occur?

(second question)
using inductive reasoning, write a formula for the number of handshakes if the number of people is n

Answer 1

combinations of n objects taken r at a time
C(n,r) = n!/[r!(n-r!)]
C(7,2) = 7!/[2!(5!)]
=7*3
=21
ok, reasoning
first person shakes with 6
second person with 5
third with 4
.
.
.
6th with 1
so
6+5+4+3+2+1 = 21 sure enough

Answer 2

49