There are 13 couples in a party. Suppose that each man shakes hand with everyone else except his own wife, and that each lady does not shake hand with other ladies. What is the total number of handshakes?
I got two solutions. Tell me which one is right and where is the mistake in the other one.
Method 1:
Total no of possible handshakes = 26C2 = 325.
Total Man-wife hand shakes = 13
Total wife-wife handshakes = 13C2 = 78
Therefore, Ans = 325 - 13 - 78 = 234
Method 2
Since the man already shakes hand with the ladies and the ladies do not shake hands with one another, We just need to count the no of handshakes from the men.
First man would shakes hand with 24 others (12 couples), 2nd man would shakes hand with the remaining 22 others (11 couples), and so on.
Total no of handshakes = 24 + 22 + 20 + 18 + 16 + ... 4 + 2 + 0 = 156
method 2 wrong.
ladies got shake the men
ok nvm. I figure out that method 2 is wrong. Thanks.