SOLUTION: On a meeting, every guest shakes hands, exactly once, with every other guest. There are 36 handshakes between the ladies and 28 between the gentlemen. The number of handshakes betw

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Question 727884: On a meeting, every guest shakes hands, exactly once, with every other guest. There are 36 handshakes between the ladies and 28 between the gentlemen. The number of handshakes between a gentleman and a lady is what?
Answer by KMST(5328) About Me  (Show Source):
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In a group of n people, if every person shakes hands with every other person exactly once, each person would report %28n-1%29 handshakes, and you would get a total of n%28n-1%29 such reports. That number would be double the number of handshakes, because it handshake would be reported twice, with one report by each of the two handshakers involved.

If there were 36 handshakes between the n ladies,
n%28n-1%29%2F2=36 --> n%28n-1%29=36%2A2 --> n%28n-1%29=9%2A4%2A2 --> n%28n-1%29=9%2A8 --> n=9. There are highlight%289%29 ladies.
If there were 28 handshakes between the m gentlemen,
m%28m-1%29%2F2=28 --> m%28m-1%29=28%2A2 --> m%28m-1%29=7%2A4%2A2 --> m%28m-1%29=7%2A8 --> m=8. There are highlight%288%29 gentlemen.

Each of the 9 ladies shakes hands with each of the 8 gentleman for a total of
9%2A8=highlight%2872%29 handshakes between a lady and a gentleman.