A Permutation Question about Handshakes?

there are 2n people

your wife shakes hands with n-1 males

you shake hands with n-1 males + n-1 females = 2n-2 people

but remember, TWO people in every handshake,

so # of handshakes = [n(n-1) + n(2n-2)]/2

= 1.5n² - 1.5n

▬▬▬▬▬▬

ps:

----

confirmation of formula for small #, say ABC (males) abc (females)

AB AC BC Ab Ac Ba Bc Ca Cb = 9 handshakes

1.5*3^2 - 1.5*3 = 9

There are n males and n females. Each person shakes hand with n-1 males(n males minus himself) and n-1 females( n females minus his wife). so total hand shakes by each person is (n-1) + (n-1) = 2(n-1). There are n men and each men shakes hand similarly so total n*2(n-1) or say 2n(n-1).