Question 861871: Seven matrons assembled for a meeting,shake hands with one another. How many handshakes take place?
Found 2 solutions by stanbon, richwmiller:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! seven matrons assembled for a meeting,shake hands with one another .
how many handshakes take place?
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Develop the pattern::
1 matron------no handshakes =
2 matrons----- 1 handshake = 2 -1
3 matrons----- 3 handshakes = 2^2-1
4 matrons------7 handshakes = 2^3-1
5 matrons------2^4-1 = 15
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7 matrons------2^6-1 = 64-1 = 63
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Cheers,
Stan H.
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Answer by richwmiller(17219)  (Show Source):
You can put this solution on YOUR website! 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
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