SOLUTION: 1 - How many handshakes can take place if there are 100 people and no one shakes hands twice? 2 - How many handshakes can take place if there are 100 married couples and husband

Question 4261: 1 - How many handshakes can take place if there are 100 people and no one shakes hands twice?
2 - How many handshakes can take place if there are 100 married couples and husbands do not shake thands with their wives and women do not shake hands with each other?
A formula for each would be most helpful. Thanks!!
Answer by khwang(438) (Show Source): You can put this solution on YOUR website!
1. How many handshakes can take place if there are 100 people and no one shakes hands twice?
Sol: It should be "no two shakes hands".
there are C(100,2) = 100*99/2 = 99*50 = 4950
2 - How many handshakes can take place if there are 100 married couples and husbands do not shake thands with their wives and women do not shake hands with each other?
Sol: Each husband can shake hands with other 99 males or other 99 females.
# of shake hands between 100 males = C(100,2) = 100*99 /2 = 4950
(Note A shakes with B is the same as B shakes with A)
# of shake hands between males and females = 100*99 = 9900
total = 4950 + 9900 = 14850.
(We don't care females shaking with males . Why ?)

Each wife can shake hands with other 99 males.

Similar a diagram below.
Male Female (5 couples for convenience)
A A'
B B'
C C'
D D'
E E'
# of shake hands between males = C(5,2) = 5*4 /2 =10
# of shake hands between males and females = 5* 4 = 20
total = 30

Forget any formulas, rely on logic and your brains.
Good luck!
Kenny
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