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