Question 861871
C(7,2) 
7*6/2=42/2=21
2 people 
1 handshake ab =ba  c(2,2)=1
3 people 
c(3,2)=ab=ba bc=cb ac =ca  3*2/2=3
4 people
c(4,2) 4*3/2=6 
ab=ba bc=cb ac=ca  ad=da bd=db cd=dc
5 people
c(5,2) 5*4/2=10
ab=ba bc=cb ac=ca  ad=da bd=db cd=dc ae=ea be=eb ce=ec de=ed
6 people 
c(6,2) 6*5/2=15
ab=ba bc=cb ac=ca  ad=da bd=db cd=dc ae=ea be=eb ce=ec de=ed
af=fa bf=fb cf=fc df=fd ef=fe

7 people 
c(7,2) 7*6/2=21
ab=ba bc=cb ac=ca  ad=da bd=db cd=dc ae=ea be=eb ce=ec de=ed
af=fa bf=fb cf=fc df=fd ef=fe ag=ga bg=gb cg=gc dg=gd eg=ge fg=gf
that is it for 7 matrons
 21 handshakes no more no less