Math Counting Problem

Twenty people are at a party. If everyone at the party shakes the hand of everyone else at the party, determine the number of handshakes.

I've figured out the answer to that question is 190 handshakes. (correct if i'm wrong)

I'm having trouble with the next part of the question though:
Ten married couples are having a party. If each person at the party shakes the hand of everyone else except his/her spouse, determine the number of handshakes at the party.

can someone help me find the solution? thank you.

1) 20C2 = 20*19/2 = 190 handshakes

2) 20C2 - 10 = 180 handshakes
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Ideas: Use complement set.

part one wrong every one shakes the hand of 19 people so 20*19=380 part two would be 20*18=360 because there is 20 people if they shake there spouses hand also it would be 19 so subtract 1 and times by 20