Five couples were at a party. If each person shook hands exactly once with everyone else except his/her spouse, how many handshakes were exchanged? (Note: One obviously doesn't shake hands with oneself.)
All ten people shake hands with everyone except his/jher spouse and themseves.
Since there are 10 people(five(5) married couples), the answer should be 10 * 8 / 2 = 40 handshakes were exchanged,
Note that dividing by two cleared the overcounting of the handshakes.
I get a little different result from tertre
Note that the
10th person shakes 9 hands
9th person shakes 8 hands
8th person shakes 7 hands
2nd person shakes 1 hand
So.....the number of handshakes seems just to be the sum of the first 9 positive integers =
9 * 10 / 2 = 45 handshakes